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Publications about 'ISS'
Articles in journal or book chapters
  1. E.D. Sontag. Input-to-State Stability. In J. Baillieul and T. Samad, editors, Encyclopedia of Systems and Control, pages 1-9. Springer-Verlag, 2020. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, input to output stability.
    Abstract:
    The notion of input to state stability (ISS) qualitatively describes stability of the mapping from initial states and inputs to internal states (and more generally outputs). This encyclopedia-style article entry gives a brief introduction to the definition of ISS and a discussion of equivalent characterizations. It is an update of the article in the 2015 edition, including additional citations to recent PDE work.


  2. J.L. Gevertz, J.M. Greene, C Hixahuary Sanchez Tapia, and E D Sontag. A novel COVID-19 epidemiological model with explicit susceptible and asymptomatic isolation compartments reveals unexpected consequences of timing social distancing. Journal of Theoretical Biology, 510:110539, 2020. [WWW] [PDF] Keyword(s): epidemiology, COVID-19, COVID, systems biology.
    Abstract:
    Motivated by the current COVID-19 epidemic, this work introduces an epidemiological model in which separate compartments are used for susceptible and asymptomatic "socially distant" populations. Distancing directives are represented by rates of flow into these compartments, as well as by a reduction in contacts that lessens disease transmission. The dynamical behavior of this system is analyzed, under various different rate control strategies, and the sensitivity of the basic reproduction number to various parameters is studied. One of the striking features of this model is the existence of a critical implementation delay in issuing separation mandates: while a delay of about four weeks does not have an appreciable effect, issuing mandates after this critical time results in a far greater incidence of infection. In other words, there is a nontrivial but tight "window of opportunity" for commencing social distancing. Different relaxation strategies are also simulated, with surprising results. Periodic relaxation policies suggest a schedule which may significantly inhibit peak infective load, but that this schedule is very sensitive to parameter values and the schedule's frequency. Further, we considered the impact of steadily reducing social distancing measures over time. We find that a too-sudden reopening of society may negate the progress achieved under initial distancing guidelines, if not carefully designed.


  3. E.D. Sontag. Input-to-State Stability. In J. Baillieul and T. Samad, editors, Encyclopedia of Systems and Control. Springer-Verlag, 2015. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, input to output stability.
    Abstract:
    The notion of input to state stability (ISS) qualitatively describes stability of the mapping from initial states and inputs to internal states (and more generally outputs). This entry focuses on the definition of ISS and a discussion of equivalent characterizations.


  4. A. Rufino Ferreira, M. Arcak, and E.D. Sontag. Stability certification of large scale stochastic systems using dissipativity of subsystems. Automatica, 48:2956-2964, 2012. [PDF] Keyword(s): stochastic systems, passivity, noise-to-state stability, ISS, input to state stability.
    Abstract:
    This paper deals with the stability of interconnections of nonlinear stochastic systems, using concepts of passivity and noise-to-state stability.


  5. E.D. Sontag. Input to State Stability. In W. S. Levine, editor, The Control Systems Handbook: Control System Advanced Methods, Second Edition., pages 45.1-45.21 (1034-1054). CRC Press, Boca Raton, 2011. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, input to output stability.
    Abstract:
    An encyclopedia-type article on foundations of ISS.


  6. E.D. Sontag. Stability and feedback stabilization. In Robert Meyers, editor, Mathematics of Complexity and Dynamical Systems, pages 1639-1652. Springer-Verlag, Berlin, 2011. [PDF] Keyword(s): stability, nonlinear control, feedback stabilization.
    Abstract:
    The problem of stabilization of equilibria is one of the central issues in control. In addition to its intrinsic interest, it represents a first step towards the solution of more complicated problems, such as the stabilization of periodic orbits or general invariant sets, or the attainment of other control objectives, such as tracking, disturbance rejection, or output feedback, all of which may be interpreted as requiring the stabilization of some quantity (typically, some sort of ``error'' signal). A very special case, when there are no inputs, is that of stability. This short and informal article provides an introduction to the subject.


  7. D. Del Vecchio and E.D. Sontag. Synthetic Biology: A Systems Engineering Perspective. In B.P. Ingalls and P. Iglesias, editors, Control Theory in Systems Biology, pages 101-123. MIT Press, 2009.
    Abstract:
    This is an expository paper about certain aspects of Synthetic Biology, including a discussion of the issue of modularity (load effects from downstream components).


  8. E.D. Sontag. Stability and Feedback Stabilization. In Robert Meyers, editor, Encyclopedia of Complexity and Systems Science. Springer-Verlag, Berlin, 2007. Keyword(s): stability, nonlinear control, feedback stabilization.
    Abstract:
    The problem of stabilization of equilibria is one of the central issues in control. In addition to its intrinsic interest, it represents a first step towards the solution of more complicated problems, such as the stabilization of periodic orbits or general invariant sets, or the attainment of other control objectives, such as tracking, disturbance rejection, or output feedback, all of which may be interpreted as requiring the stabilization of some quantity (typically, some sort of ``error'' signal). A very special case, when there are no inputs, is that of stability. This short and informal article provides an introduction to the subject.


  9. P. Berman, B. Dasgupta, and E.D. Sontag. Algorithmic issues in reverse engineering of protein and gene networks via the modular response analysis method. Annals of the NY Academy of Sciences, 1115:132-141, 2007. [PDF] Keyword(s): systems biology, biochemical networks, gene and protein networks, reverse engineering, systems identification, graph algorithms.
    Abstract:
    This paper studies a computational problem motivated by the modular response analysis method for reverse engineering of protein and gene networks. This set-cover problem is hard to solve exactly for large networks, but efficient approximation algorithms are given and their complexity is analyzed.


  10. M. Malisoff and E.D. Sontag. Asymptotic controllability and input-to-state stabilization: the effect of actuator errors. In Optimal control, stabilization and nonsmooth analysis, volume 301 of Lecture Notes in Control and Inform. Sci., pages 155-171. Springer, Berlin, 2004. [PDF] Keyword(s): input to state stability, control-Lyapunov functions, nonlinear control, feedback stabilization, ISS.
    Abstract:
    We discuss several issues related to the stabilizability of nonlinear systems. First, for continuously stabilizable systems, we review constructions of feedbacks that render the system input-to-state stable with respect to actuator errors. Then, we discuss a recent paper which provides a new feedback design that makes globally asymptotically controllable systems input-to-state stable to actuator errors and small observation noise. We illustrate our constructions using the nonholonomic integrator, and discuss a related feedback design for systems with disturbances.


  11. D. Angeli, B.P. Ingalls, E.D. Sontag, and Y. Wang. Separation principles for input-output and integral-input-to-state stability. SIAM J. Control Optim., 43(1):256-276, 2004. [PDF] [doi:http://dx.doi.org/10.1137/S0363012902419047] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, input to output stability.
    Abstract:
    We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of asymptotic estimates of the state trajectories based on the magnitudes of the external input and output signals. These results provide a set of "separation principles" for input-output-to-state stability , characterizations of the property in terms of weaker stability notions. When applied to the closely related notion of integral ISS, these characterizations yield analogous results.


  12. D. Angeli, E.D. Sontag, and Y. Wang. Input-to-state stability with respect to inputs and their derivatives. Internat. J. Robust Nonlinear Control, 13(11):1035-1056, 2003. [PDF] Keyword(s): input to state stability, ISS, input to state stability, ISS.
    Abstract:
    A new notion of input-to-state stability involving infinity norms of input derivatives up to a finite order k is introduced and characterized. An example shows that this notion of stability is indeed weaker than the usual ISS. Applications to the study of global asymptotic stability of cascaded nonlinear systems are discussed.


  13. M. Arcak, D. Angeli, and E.D. Sontag. A unifying integral ISS framework for stability of nonlinear cascades. SIAM J. Control Optim., 40(6):1888-1904, 2002. [PDF] [doi:http://dx.doi.org/10.1137/S0363012901387987] Keyword(s): input to state stability, integral input to state stability, iISS, ISS.
    Abstract:
    We analyze nonlinear cascades in which the driven subsystem is integral ISS, and characterize the admissible integral ISS gains for stability. This characterization makes use of the convergence speed of the driving subsystem, and allows a larger class of gain functions when the convergence is faster. We show that our integral ISS gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem.


  14. D. Liberzon, A. S. Morse, and E.D. Sontag. Output-input stability and minimum-phase nonlinear systems. IEEE Trans. Automat. Control, 47(3):422-436, 2002. [PDF] Keyword(s): input to state stability, detectability, minimum-phase systems, ISS, nonlinear control, minimum phase, adaptive control.
    Abstract:
    This paper introduces and studies a new definition of the minimum-phase property for general smooth nonlinear control systems. The definition does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of minimum-phase systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control.


  15. D. Liberzon, E.D. Sontag, and Y. Wang. Universal construction of feedback laws achieving ISS and integral-ISS disturbance attenuation. Systems Control Lett., 46(2):111-127, 2002. Note: Errata here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/iiss-clf-errata.pdf. [PDF] Keyword(s): input to state stability, integral input to state stability, ISS, iISS, nonlinear control, feedback stabilization.
    Abstract:
    We study nonlinear systems with both control and disturbance inputs. The main problem addressed in the paper is design of state feedback control laws that render the closed-loop system integral-input-to-state stable (iISS) with respect to the disturbances. We introduce an appropriate concept of control Lyapunov function (iISS-CLF), whose existence leads to an explicit construction of such a control law. The same method applies to the problem of input-to-state stabilization. Converse results and techniques for generating iISS-CLFs are also discussed.


  16. E.D. Sontag and B.P. Ingalls. A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections. J. Franklin Inst., 339(2):211-229, 2002. [PDF] Keyword(s): input to state stability, ISS, Small-Gain Theorem.
    Abstract:
    A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems.


  17. E.D. Sontag. The ISS philosophy as a unifying framework for stability-like behavior. In Nonlinear control in the year 2000, Vol. 2 (Paris), volume 259 of Lecture Notes in Control and Inform. Sci., pages 443-467. Springer, London, 2001. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, input to output stability.
    Abstract:
    (This is an expository paper prepared for a plenary talk given at the Second Nonlinear Control Network Workshop, Paris, June 9, 2000.) The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical results concerning ISS and related notions of input/output stability and detectability. A bibliography is also included, listing extensions, applications, and other current work.


  18. B. DasGupta and E.D. Sontag. A polynomial-time algorithm for checking equivalence under certain semiring congruences motivated by the state-space isomorphism problem for hybrid systems. Theor. Comput. Sci., 262(1-2):161-189, 2001. [PDF] [doi:http://dx.doi.org/10.1016/S0304-3975(00)00188-2] Keyword(s): hybrid systems, computational complexity.
    Abstract:
    The area of hybrid systems concerns issues of modeling, computation, and control for systems which combine discrete and continuous components. The subclass of piecewise linear (PL) systems provides one systematic approach to discrete-time hybrid systems, naturally blending switching mechanisms with classical linear components. PL systems model arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic, and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a "PL algebra" formalism. PL systems are of interest as controllers as well as identification models. Basic questions for any class of systems are those of equivalence, and, in particular, if state spaces are equivalent under a change of variables. This paper studies this state-space equivalence problem for PL systems. The problem was known to be decidable, but its computational complexity was potentially exponential; here it is shown to be solvable in polynomial-time.


  19. D. Angeli, E.D. Sontag, and Y. Wang. A characterization of integral input-to-state stability. IEEE Trans. Automat. Control, 45(6):1082-1097, 2000. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS.
    Abstract:
    Just as input to state stability (ISS) generalizes the idea of finite gains with respect to supremum norms, the new notion of integral input to state stability (IISS) generalizes the concept of finite gain when using an integral norm on inputs. In this paper, we obtain a necessary and sufficient characterization of the IISS property, expressed in terms of dissipation inequalities.


  20. D. Angeli, E.D. Sontag, and Y. Wang. Further equivalences and semiglobal versions of integral input to state stability. Dynamics and Control, 10(2):127-149, 2000. [PDF] [doi:http://dx.doi.org/10.1023/A:1008356223747] Keyword(s): input to state stability, integral input to state stability, iISS, ISS.
    Abstract:
    This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the superposition of a ``bounded energy bounded state'' requirement and the global asymptotic stability of the unforced system. A semiglobal version of IISS is shown to imply the global version, though a counterexample shows that the analogous fact fails for input to state stability (ISS). The results in this note complete the basic theoretical picture regarding IISS and ISS.


  21. X. Bao, Z. Lin, and E.D. Sontag. Finite gain stabilization of discrete-time linear systems subject to actuator saturation. Automatica, 36(2):269-277, 2000. [PDF] Keyword(s): discrete-time, saturation, input-to-state stability, stabilization, ISS, bounded inputs.
    Abstract:
    It is shown that, for neutrally stable discrete-time linear systems subject to actuator saturation, finite gain lp stabilization can be achieved by linear output feedback, for all p>1. An explicit construction of the corresponding feedback laws is given. The feedback laws constructed also result in a closed-loop system that is globally asymptotically stable, and in an input-to-state estimate.


  22. E.D. Sontag. Stability and stabilization: discontinuities and the effect of disturbances. In Nonlinear analysis, differential equations and control (Montreal, QC, 1998), volume 528 of NATO Sci. Ser. C Math. Phys. Sci., pages 551-598. Kluwer Acad. Publ., Dordrecht, 1999. [PDF] Keyword(s): feedback stabilization, nonlinear control, input to state stability.
    Abstract:
    In this expository paper, we deal with several questions related to stability and stabilization of nonlinear finite-dimensional continuous-time systems. We review the basic problem of feedback stabilization, placing an emphasis upon relatively new areas of research which concern stability with respect to "noise" (such as errors introduced by actuators or sensors). The table of contents is as follows: Review of Stability and Asymptotic Controllability, The Problem of Stabilization, Obstructions to Continuous Stabilization, Control-Lyapunov Functions and Artstein's Theorem, Discontinuous Feedback, Nonsmooth CLF's, Insensitivity to Small Measurement and Actuator Errors, Effect of Large Disturbances: Input-to-State Stability, Comments on Notions Related to ISS.


  23. L. Grüne, E.D. Sontag, and F.R. Wirth. Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes. Systems Control Lett., 38(2):127-134, 1999. [PDF] Keyword(s): input to state stability, ISS.
    Abstract:
    This paper shows that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown respectively for input-to-state stability, input-to-state exponential stability, and the property of finite square-norm gain ("nonlinear H-infty"). The results are shown for systems of any dimension not equal to 4 or 5.


  24. D. Nesic, A.R. Teel, and E.D. Sontag. Formulas relating KL stability estimates of discrete-time and sampled-data nonlinear systems. Systems Control Lett., 38(1):49-60, 1999. [PDF] Keyword(s): input to state stability, sampled-data systems, discrete-time systems, sampling, ISS.
    Abstract:
    We provide an explicit KL stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the KL estimate for the corresponding discrete-time system and a K function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system; our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results of Aeyels et al and extend some results by Chen et al to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate.


  25. E.D. Sontag and Y. Wang. Notions of input to output stability. Systems Control Lett., 38(4-5):235-248, 1999. [PDF] Keyword(s): input to state stability, ISS, input to output stability.
    Abstract:
    This paper deals with several related notions of output stability with respect to inputs (which may be thought of as disturbances). The main such notion is called input to output stability (IOS), and it reduces to input to state stability (ISS) when the output equals the complete state. For systems with no inputs, IOS provides a generalization of the classical concept of partial stability. Several variants, which formalize in different manners the transient behavior, are introduced. The main results provide a comparison among these notions


  26. D. Nesic and E.D. Sontag. Input-to-state stabilization of linear systems with positive outputs. Systems Control Lett., 35(4):245-255, 1998. [PDF] Keyword(s): input to state stability, ISS, stabilization.
    Abstract:
    This paper considers the problem of stabilization of linear systems for which only the magnitudes of outputs are measured. It is shown that, if a system is controllable and observable, then one can find a stabilizing controller, which is robust with respect to observation noise (in the ISS sense).


  27. E.D. Sontag. Comments on integral variants of ISS. Systems Control Lett., 34(1-2):93-100, 1998. [PDF] [doi:http://dx.doi.org/10.1016/S0167-6911(98)00003-6] Keyword(s): input to state stability, integral input to state stability, iISS, ISS.
    Abstract:
    This note discusses two integral variants of the input-to-state stability (ISS) property, which represent nonlinear generalizations of L2 stability, in much the same way that ISS generalizes L-infinity stability. Both variants are equivalent to ISS for linear systems. For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. For bilinear systems, a complete characterization is provided of the weaker property. An interesting fact about functions of type KL is proved as well.


  28. E.D. Sontag and Y. Wang. Output-to-state stability and detectability of nonlinear systems. Systems Control Lett., 29(5):279-290, 1997. [PDF] [doi:http://dx.doi.org/10.1016/S0167-6911(97)90013-X] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, detectability, output to state stability, detectability, input to state stability.
    Abstract:
    The notion of input-to-state stability (ISS) has proved to be useful in nonlinear systems analysis. This paper discusses a dual notion, output-to-state stability (OSS). A characterization is provided in terms of a dissipation inequality involving storage (Lyapunov) functions. Combining ISS and OSS there results the notion of input/output-to-state stability (IOSS), which is also studied and related to the notion of detectability, the existence of observers, and output injection.


  29. E.D. Sontag and Y. Wang. New characterizations of input-to-state stability. IEEE Trans. Automat. Control, 41(9):1283-1294, 1996. [PDF] Keyword(s): input to state stability, ISS.
    Abstract:
    We present new characterizations of the Input to State Stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variations proposed in the literature.


  30. Y. Lin, E.D. Sontag, and Y. Wang. Input to state stabilizability for parametrized families of systems,ISS,stabilization. Internat. J. Robust Nonlinear Control, 5(3):187-205, 1995. [PDF]
    Abstract:
    This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov-theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state space stability to ``input to state'' (bounded-input bounded-state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analyzed.


  31. E.D. Sontag. On the input-to-state stability property. European J. Control, 1:24-36, 1995. [PDF] Keyword(s): input to state stability, ISS.
    Abstract:
    The "input to state stability" (ISS) property provides a natural framework in which to formulate notions of stability with respect to input perturbations. In this expository paper, we review various equivalent definitions expressed in stability, Lyapunov-theoretic, and dissipation terms. We sketch some applications to the stabilization of cascades of systems and of linear systems subject to control saturation.


  32. E.D. Sontag and A.R. Teel. Changing supply functions in input/state stable systems. IEEE Trans. Automat. Control, 40(8):1476-1478, 1995. [PDF] Keyword(s): input to state stability, ISS, input to state stability, Lyapunov functions.
    Abstract:
    We consider the problem of characterizing possible supply functions for a given dissipative nonlinear system, and provide a result that allows some freedom in the modification of such functions.


  33. E.D. Sontag and Y. Wang. On characterizations of the input-to-state stability property. Systems Control Lett., 24(5):351-359, 1995. [PDF] [doi:http://dx.doi.org/10.1016/0167-6911(94)00050-6] Keyword(s): input to state stability, ISS.
    Abstract:
    We show that the well-known Lyapunov sufficient condition for input-to-state stability is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.


  34. E.D. Sontag. Further facts about input to state stabilization. IEEE Trans. Automat. Control, 35(4):473-476, 1990. [PDF] Keyword(s): input to state stability, ISS, stabilization.
    Abstract:
    Previous results about input to state stabilizability are shown to hold even for systems which are not linear in controls, provided that a more general type of feedback be allowed. Applications to certain stabilization problems and coprime factorizations, as well as comparisons to other results on input to state stability, are also briefly discussed.d local minima may occur, if the data are not separable and sigmoids are used.


  35. E.D. Sontag. Smooth stabilization implies coprime factorization. IEEE Trans. Automat. Control, 34(4):435-443, 1989. [PDF] Keyword(s): input to state stability, ISS, input to state stability.
    Abstract:
    This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. In order to establish the result a Lyapunov-theoretic definition is proposed for bounded input bounded output stability. The main technical fact proved relates the notion of stabilizability studied in the state space nonlinear control literature to a notion of stability under bounded control perturbations analogous to those studied in operator theoretic approaches to systems; it states that smooth stabilization implies smooth input-to-state stabilization. (Note: This is the original ISS paper, but the ISS results have been much improved in later papers. The material on coprime factorizations is still of interest, but the 89 CDC paper has some improvements and should be read too.)


Conference articles
  1. A. O. Hamadeh, E.D. Sontag, and D. Del Vecchio. A contraction approach to output tracking via high-gain feedback. In Proc. IEEE Conf. Decision and Control, Dec. 2015, pages 7689-7694, 2015. [PDF]
    Abstract:
    This paper adopts a contraction approach to the analysis of the tracking properties of dynamical systems under high gain feedback when subject to inputs with bounded derivatives. It is shown that if the tracking error dynamics are contracting, then the system is input to output stable with respect to the input signal derivatives and the output tracking error. As an application, it iss hown that the negative feedback connection of plants composed of two strictly positive real LTI subsystems in cascade can follow external inputs with tracking errors that can be made arbitrarily small by applying a sufficiently large feedback gain. We utilize this result to design a biomolecular feedback for a synthetic genetic sensor to make it robust to variations in the availability of a cellular resource required for protein production.


  2. D. Angeli, E.D. Sontag, and Y. Wang. A note on input-to-state stability with input derivatives. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 720-725, 2001. Keyword(s): input to state stability, ISS.


  3. E.D. Sontag, B.P. Ingalls, and Y. Wang. Generalizations of asymptotic gain characterizations of ISS to input-to-output stability. In Proc. American Control Conf., Arlington, June 2001, pages 2279-2284, 2001. Keyword(s): input to state stability, ISS.


  4. L. Grune, E.D. Sontag, and F.R. Wirth. On the equivalence between asymptotic and exponential stability, and between ISS and finite H infinity gain. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 1220-1225, 1999. Keyword(s): input to state stability.


  5. Z-P. Jiang, E.D. Sontag, and Y. Wang. Input-to-state stability for discrete-time nonlinear systems. In Proc. 14th IFAC World Congress, Vol E (Beijing), pages 277-282, 1999. [PDF] Keyword(s): input to state stability, input to state stability, ISS, discrete-time.
    Abstract:
    This paper studies the input-to-state stability (ISS) property for discrete-time nonlinear systems. We show that many standard ISS results may be extended to the discrete-time case. More precisely, we provide a Lyapunov-like sufficient condition for ISS, and we show the equivalence between the ISS property and various other properties, as well as provide a small gain theorem.


  6. M. Krichman, E.D. Sontag, and Y. Wang. Lyapunov characterizations of input-ouput-to-state stability. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 2070-2075, 1999. Keyword(s): input to state stability, ISS, detectability.


  7. D. Liberzon, E.D. Sontag, and Y. Wang. On integral-input-to-state stabilization. In Proc. American Control Conf., San Diego, June 1999, pages 1598-1602, 1999. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, control-Lyapunov functions.
    Abstract:
    This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance attenuation. The main contribution is an appropriate concept of control Lyapunov function (iISS-CLF), whose existence leads to an explicit construction of such a control law. The results are compared and contrasted with the ones available for the ISS case.


  8. E.D. Sontag. Notions of integral input-to-state stability. In Proc. American Control Conf., Philadelphia, June 1998, pages 3215-321, 1998. Keyword(s): input to state stability, integral input to state stability, iISS, ISS.


  9. E.D. Sontag and Y. Wang. A notion of input to output stability. In Proc. European Control Conf., Brussels, July 1997, 1997. Note: (Paper WE-E A2, CD-ROM file ECC958.pdf, 6 pages). [PDF] Keyword(s): input to state stability, ISS, input to output stability, input to state stability.
    Abstract:
    This paper deals with a notion of "input to output stability (IOS)", which formalizes the idea that outputs depend in an "aymptotically stable" manner on inputs, while internal signals remain bounded. When the output equals the complete state, one recovers the property of input to state stability (ISS). When there are no inputs, one has a generalization of the classical concept of partial stability. The main results provide Lyapunov-function characterizations of IOS.


  10. E.D. Sontag and Y. Wang. Detectability of nonlinear systems. In Proc. Conf. on Information Sciences and Systems (CISS 96), Princeton, NJ, pages 1031-1036, 1996. [PDF] Keyword(s): detectability, input to state stability, ISS.
    Abstract:
    Contains a proof of a technical step, which was omitted from the journal paper due to space constraints


  11. E.D. Sontag and Y. Wang. On characterizations of input-to-state stability with respect to compact sets. In Proceedings of IFAC Non-Linear Control Systems Design Symposium, (NOLCOS '95), Tahoe City, CA, June 1995, pages 226-231, 1995. [PDF] Keyword(s): input to state stability, ISS.
    Abstract:
    Previous characterizations of ISS-stability are shown to generalize without change to the case of stability with respect to sets. Some results on ISS-stabilizability are mentioned as well.


  12. E.D. Sontag and Y. Wang. Various results concerning set input-to-state stability. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 1330-1335, 1995. Keyword(s): input to state stability, ISS.


  13. E.D. Sontag and Y. Wang. Notions equivalent to input-to-state stability. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 3438-3443, 1994. Keyword(s): input to state stability, ISS.


  14. E.D. Sontag. Remarks on stabilization and input-to-state stability. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989), New York, pages 1376-1378, 1989. IEEE. [PDF] Keyword(s): input to state stability, ISS, stabilization.
    Abstract:
    This paper describes how notions of input-to-state stabilization are useful when stabilizing cascades of systems. The simplest result along these lines is local, and it states that a cascade of two locally asymptotically stable systems is again asystable. A global result is obtained if both systems have the origin as a globally asymptotically stable state and the "converging input bounded state" property holds for the second system. Relations to input to state stability and the "bounded input bounded state" property as mentioned as well.



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