Publications about 'linear systems'
Books and proceedings
  1. E.D. Sontag. Polynomial Response Maps, volume 13 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, 1979. [PDF] Keyword(s): realization theory, discrete-time, real algebraic geometry.
    (This is a monograph based upon Eduardo Sontag's Ph.D. thesis. The contents are basically the same as the thesis, except for a very few revisions and extensions.) This work deals the realization theory of discrete-time systems (with inputs and outputs, in the sense of control theory) defined by polynomial update equations. It is based upon the premise that the natural tools for the study of the structural-algebraic properties (in particular, realization theory) of polynomial input/output maps are provided by algebraic geometry and commutative algebra, perhaps as much as linear algebra provides the natural tools for studying linear systems. Basic ideas from algebraic geometry are used throughout in system-theoretic applications (Hilbert's basis theorem to finite-time observability, dimension theory to minimal realizations, Zariski's Main Theorem to uniqueness of canonical realizations, etc). In order to keep the level elementary (in particular, not utilizing sheaf-theoretic concepts), certain ideas like nonaffine varieties are used only implicitly (eg., quasi-affine as open sets in affine varieties) or in technical parts of a few proofs, and the terminology is similarly simplified (e.g., "polynomial map" instead of "scheme morphism restricted to k-points", or "k-space" instead of "k-points of an affine k-scheme").

Articles in journal or book chapters
  1. M.A. Al-Radhawi, D. Angeli, and E.D. Sontag. A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks. PLoS Computational Biology, pp 16(2): e1007681, 2020. [PDF] Keyword(s): MAPK cascades, Lyapunov functions, stability, chemical networks, chemical rection networks, systems biology, RFM, ribosome flow model.
    This paper deals with the analysis of the dynamics of chemical reaction networks, developing a theoretical framework based only on graphical knowledge and applying regardless of the particular form of kinetics. This paper introduces a class of networks that are "structurally (mono) attractive", by which we mean that they are incapable of exhibiting multiple steady states, oscillation, or chaos by the virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function which we call a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided that constructs such functions or rules out their existence. An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. We study basic motifs, three-body binding, and transcriptional networks. We focus on cellular signalling networks including various post-translational modification cascades, phosphotransfer and phosphorelay networks, T-cell kinetic proofreading, ERK signaling, and the Ribosome Flow Model.

  2. E.D. Sontag. Passivity gains and the ``secant condition'' for stability. Systems Control Lett., 55(3):177-183, 2006. [PDF] Keyword(s): cyclic feedback systems, systems biology, biochemical networks, nonlinear stability, dynamical systems, passive systems, secant condition, biochemical networks.
    A generalization of the classical secant condition for the stability of cascades of scalar linear systems is provided for passive systems. The key is the introduction of a quantity that combines gain and phase information for each system in the cascade. For linear one-dimensional systems, the known result is recovered exactly.

  3. M. Chaves, R.J. Dinerstein, and E.D. Sontag. Optimal length and signal amplification in weakly activated signal transduction cascades. J. Physical Chemistry, 108:15311-15320, 2004. [PDF] Keyword(s): systems biology, biochemical networks, dynamical systems.
    Weakly activated signaling cascades can be modeled as linear systems. The input-to-output transfer function and the internal gain of a linear system, provide natural measures for the propagation of the input signal down the cascade and for the characterization of the final outcome. The most efficient design of a cascade for generating sharp signals, is obtained by choosing all the off rates equal, and a "universal" finite optimal length.

  4. P. Kuusela, D. Ocone, and E.D. Sontag. Learning Complexity Dimensions for a Continuous-Time Control System. SIAM J. Control Optim., 43(3):872-898, 2004. [PDF] [doi:] Keyword(s): machine learning, theory of computing and complexity, VC dimension, neural networks.
    This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no greater than n. The main result establishes that the sample complexity needed for identification scales polynomially with n and logarithmically with k.

  5. 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.
    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.

  6. 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.
    (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.

  7. 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:] Keyword(s): hybrid systems, computational complexity.
    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.

  8. 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.
    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.

  9. 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.
    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).

  10. E.D. Sontag. Comments on integral variants of ISS. Systems Control Lett., 34(1-2):93-100, 1998. [PDF] [doi:] Keyword(s): input to state stability, integral input to state stability, iISS, ISS.
    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.

  11. E.D. Sontag. Interconnected automata and linear systems: a theoretical framework in discrete-time. In R. Alur, T.A. Henzinger, and E.D. Sontag, editors, Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control, pages 436-448. Springer-Verlag New York, Inc., Secaucus, NJ, USA, 1996. [PDF] Keyword(s): hybrid systems.
    This paper summarizes the definitions and several of the main results of an approach to hybrid systems, which combines finite automata and linear systems, developed by the author in the early 1980s. Some related more recent results are briefly mentioned as well.

  12. W. Liu, Y. Chitour, and E.D. Sontag. On finite-gain stabilizability of linear systems subject to input saturation. SIAM J. Control Optim., 34(4):1190-1219, 1996. [PDF] [doi:] Keyword(s): saturation, bounded inputs.
    This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every Lp-norm. Explicit bounds on closed-loop gains are obtained, and they are related to the norms for the respective systems without saturation. These results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple (size >1) Jordan blocks, contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state-space sense; this is shown in particular for the double integrator.

  13. Y. Chitour, W. Liu, and E.D. Sontag. On the continuity and incremental-gain properties of certain saturated linear feedback loops. Internat. J. Robust Nonlinear Control, 5(5):413-440, 1995. [PDF] Keyword(s): saturation, bounded inputs, incremental gains.
    This paper discusses various continuity and incremental-gain properties for neutrally stable linear systems under linear feedback subject to actuator saturation. The results complement our previous ones, which applied to the same class of problems and provided finite-gain stability.

  14. 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.
    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.

  15. R. Koplon, E.D. Sontag, and M. L. J. Hautus. Observability of linear systems with saturated outputs. Linear Algebra Appl., 205/206:909-936, 1994. [PDF] Keyword(s): observability, saturation, bounded inputs.
    In this paper, we present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function before it can be measured.

  16. H.J. Sussmann, E.D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. IEEE Trans. Automat. Control, 39(12):2411-2425, 1994. [PDF] Keyword(s): saturation, neural networks, global stability, nonlinear stability, bounded inputs.
    We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a "neural-network type" one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations.

  17. R. Koplon and E.D. Sontag. Linear systems with sign-observations. SIAM J. Control Optim., 31(5):1245-1266, 1993. [PDF] [doi:] Keyword(s): observability.
    This paper deals with systems that are obtained from linear time-invariant continuous- or discrete-time devices followed by a function that just provides the sign of each output. Such systems appear naturally in the study of quantized observations as well as in signal processing and neural network theory. Results are given on observability, minimal realizations, and other system-theoretic concepts. Certain major differences exist with the linear case, and other results generalize in a surprisingly straightforward manner.

  18. E.D. Sontag. Kalman's controllability rank condition: from linear to nonlinear. In Mathematical system theory, pages 453-462. Springer, Berlin, 1991. [PDF] Keyword(s): controllability.
    The notion of controllability was identified by Kalman as one of the central properties determining system behavior. His simple rank condition is ubiquitous in linear systems analysis. This article presents an elementary and expository overview of the generalizations of this test to a condition for testing accessibility of discrete and continuous time nonlinear systems.

  19. E.D. Sontag and Y. Wang. Pole shifting for families of linear systems depending on at most three parameters. Linear Algebra Appl., 137/138:3-38, 1990. [PDF] Keyword(s): systems over rings, systems over rings.
    We prove that for any family of n-dimensional controllable linear systems, continuously parameterized by up to three parameters, and for any continuous selection of n eigenvalues (in complex conjugate pairs), there is some dynamic controller of dimension 3n which is itself continuously parameterized and for which the closed-loop eigenvalues are these same eigenvalues, each counted 4 times. An analogous result holds also for smooth parameterizations.

  20. E.D. Sontag. An introduction to the stabilization problem for parametrized families of linear systems. In Linear algebra and its role in systems theory (Brunswick, Maine, 1984), volume 47 of Contemp. Math., pages 369-400. Amer. Math. Soc., Providence, RI, 1985. [PDF] Keyword(s): systems over rings.
    This paper provides an introduction to definitions and known facts relating to the stabilization of parametrized families of linear systems using static and dynamic controllers. New results are given in the rational and polynomial cases.

  21. E.D. Sontag. An algebraic approach to bounded controllability of linear systems. Internat. J. Control, 39(1):181-188, 1984. [PDF] Keyword(s): saturation, bounded inputs.
    In this note we present an algebraic approach to the proof that a linear system with matrices (A,B) is null-controllable using bounded inputs iff it is null-controllable (with unbounded inputs) and all eigenvalues of A have nonpositive real parts (continuous time) or magnitude not greater than one (discrete time). We also give the analogous results for the asymptotic case. Finally, we give an interpretation of these results in the context of local nonlinear controllability.

  22. E.D. Sontag. Parametric stabilization is easy. Systems Control Lett., 4(4):181-188, 1984. [PDF] Keyword(s): systems over rings.
    A polynomially parametrized family of continuous-time controllable linear systems is always stabilizable by polynomially parametrized feedback. (Note: appendix had a MACSYMA computation. I cannot find the source file for that. Please look at journal if interested, but this is not very important. Also, two figures involving root loci are not in the web version.)

  23. R.T. Bumby and E.D. Sontag. Stabilization of polynomially parametrized families of linear systems. The single-input case. Systems Control Lett., 3(5):251-254, 1983. [PDF] Keyword(s): systems over rings.
    Given a continuous-time family of finite dimensional single input linear systems, parametrized polynomially, such that each of the systems in the family is controllable, there exists a polynomially parametrized control law making each of the systems in the family stable.

  24. E.D. Sontag. Linear systems over commutative rings: a (partial) updated survey. In Control science and technology for the progress of society, Vol. 1 (Kyoto, 1981), pages 325-330. IFAC, Laxenburg, 1982. Keyword(s): systems over rings.

  25. P.P. Khargonekar and E.D. Sontag. On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings. IEEE Trans. Automat. Control, 27(3):627-638, 1982. [PDF] Keyword(s): systems over rings.
    Various types of transfer matrix factorizations are of interest when designing regulators for generalized types of linear systems (delay differential. 2-D, and families of systems). This paper studies the existence of stable and of stable proper factorizations, in the context of the thery of systems over rings. Factorability is related to stabilizability and detectability properties of realizations of the transfer matrix. The original formulas for coprime factorizations (which are valid, in particular, over the field of reals) were given in this paper.

  26. E.D. Sontag. Remarks on piecewise-linear algebra. Pacific J. Math., 98(1):183-201, 1982. [PDF] Keyword(s): hybrid systems, piecewise linear systems.
    Algebraic study of functions defined by piecewise linear (generally discontinuous) equations. File obtained by scanning a reprint.

  27. E.D. Sontag. Nonlinear regulation: the piecewise linear approach. IEEE Trans. Automat. Control, 26(2):346-358, 1981. [PDF] Keyword(s): hybrid systems.
    Development of an approach to nonlinear control based on mixtures of linear systems and finite automata. File obtained by scanning.

  28. M. L. J. Hautus and E.D. Sontag. An approach to detectability and observers. In Algebraic and geometric methods in linear systems theory (AMS-NASA-NATO Summer Sem., Harvard Univ., Cambridge, Mass., 1979), volume 18 of Lectures in Appl. Math., pages 99-135. Amer. Math. Soc., Providence, R.I., 1980. [PDF] Keyword(s): observability.
    This paper proposes an approach to the problem of establishing the existence of observers for deterministic dynamical systems. This approach differs from the standard one based on Luenberger observers in that the observation error is not required to be Markovian given the past input and output data. A general abstract result is given, which special- izes to new results for parametrized families of linear systems, delay systems and other classes of systems. Related problems of feedback control and regulation are also studied.

  29. E.D. Sontag. On the length of inputs necessary in order to identify a deterministic linear system. IEEE Trans. Automat. Control, 25(1):120-121, 1980. [PDF]
    The family of m-input, n-dimensional linear systems can be globally Identified with a generic input sequence of length 2mn. This bound is the best possible. A best bound is proved also for a corresponding local identification problem.

  30. E.D. Sontag. On finitary linear systems. Kybernetika (Prague), 15(5):349-358, 1979. [PDF] Keyword(s): systems over rings.
    An abstract operator approach is introduced, permitting a unified study of discrete- and continuous-time linear control systems. As an application, an algorithm is given for deciding if a linear system can be built from any fixed set of linear components. Finally, a criterion is given for reachability of the abstract systems introduced, giving thus a unified proof of known reachability results for discrete-time, continuous-time, and delay-differential systems.

  31. E.D. Sontag. Linear systems over commutative rings: A survey. Ricerche di Automatica, 7:1-34, 1976. [PDF] Keyword(s): systems over rings.
    An elementary presentation is given of some of the main motivations and known results on linear systems over rings, including questions of realization and control. The analogies and differences with the more standard case of systems over fields are emphasized throughout.

  32. E.D. Sontag. On linear systems and noncommutative rings. Math. Systems Theory, 9(4):327-344, 1975. [PDF] Keyword(s): systems over rings.
    This paper studies some problems appearing in the extension of the theory of linear dynamical systems to the case in which parameters are taken from noncommutative rings. Purely algebraic statements of some of the problems are also obtained. Through systems defined by operator rings, the theory of linear systems over rings may be applied to other areas of automata and control theory; several such applications are outlined.

Conference articles
  1. Z. Liu, N. Ozay, and E.D. Sontag. On the non-existence of immersions for systems with multiple omega-limit sets. In Proceedings of IFAC 2023 World Congress, pages 81-85, 2023. [PDF] Keyword(s): linear systems, nonlinear systems, observables, Koopman embedding, duality.
    Linear immersions (or Koopman eigenmappings) of a nonlinear system have wide applications in prediction and control. In this work, we study the existence of one-to-one linear immersions for nonlinear systems with multiple omega-limit sets. For this class of systems, existing work shows that a discontinuous one-to-one linear immersion may exist, but it is unclear if a continuous one-to-one linear immersion exists. Under mild conditions, we prove that systems with multiple omega-limit sets cannot admit a continuous one-to-one immersion to a class of systems including linear systems.

  2. B. Andrews, P. Iglesias, and E.D. Sontag. Signal detection and approximate adaptation implies an approximate internal model. In Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006, pages 2364-2369, 2006. IEEE. [PDF] Keyword(s): biological adaptation, internal model principle.
    This conference paper presented a version of an approximate internal model principle, for linear systems. A subsequent paper at the IFAC 2008 conference improved on this result by extending it to a class of nonlinear systems.

  3. X. Bao, Z. Lin, and E.D. Sontag. Some new results on finite gain $l_p$ stabilization of discrete-time linear systems subject to actuator saturation. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 4628-4629, 1998. Keyword(s): saturation, bounded inputs.

  4. D. Nesic and E.D. Sontag. Output stabilization of nonlinear systems: Linear systems with positive outputs as a case study. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 885-890, 1998.

  5. E.D. Sontag. From linear to nonlinear: some complexity comparisons. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 2916-2920, 1995. [PDF] Keyword(s): theory of computing and complexity, computational complexity, controllability, observability.
    This paper deals with the computational complexity, and in some cases undecidability, of several problems in nonlinear control. The objective is to compare the theoretical difficulty of solving such problems to the corresponding problems for linear systems. In particular, the problem of null-controllability for systems with saturations (of a "neural network" type) is mentioned, as well as problems regarding piecewise linear (hybrid) systems. A comparison of accessibility, which can be checked fairly simply by Lie-algebraic methods, and controllability, which is at least NP-hard for bilinear systems, is carried out. Finally, some remarks are given on analog computation in this context.

  6. R. Koplon and E.D. Sontag. Sign-linear systems as cascades of automata and continuous variable systems. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 2290-2291, 1993.

  7. W. Liu, Y. Chitour, and E.D. Sontag. Remarks on finite gain stabilizability of linear systems subject to input saturation. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 1808-1813, 1993. Keyword(s): saturation, bounded inputs.

  8. H.J. Sussmann, E.D. Sontag, and Y. Yang. A general result on the stabilization of linear systems using bounded controls. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 1802-1807, 1993. Keyword(s): saturation, bounded inputs.

  9. Y. Yang, H.J. Sussmann, and E.D. Sontag. Stabilization of linear systems with bounded controls. In Nonlinear Control Systems Design 1992, IFAC Symposia Series, 1993, M. Fliess Ed., Pergamon Press, Oxford, 1993, pages 51-56, 1992. Note: Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M. Fliess, Ed.), IFAC Publications, pp. 15-20.Keyword(s): saturation, bounded inputs.

  10. R. Schwarzschild and E.D. Sontag. Algebraic theory of sign-linear systems. In Proc. Amer. Automatic Control Conf., Boston, June 1991, pages 799-804, 1991.

  11. R. Schwarzschild and E.D. Sontag. Quantized systems, saturated measurements, and sign-linear systems. In Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991, pages 134-139, 1991. Keyword(s): observability, saturation.

  12. E.D. Sontag and Y. Wang. I/O equations for nonlinear systems and observation spaces. In Proc. IEEE Conf. Decision and Control, Brighton, UK, Dec. 1991, IEEE Publications, 1991, pages 720-725, 1991. [PDF] Keyword(s): identifiability, observability, realization theory, real-analytic functions.
    This paper studies various types of input/output representations for nonlinear continuous time systems. The algebraic and analytic i/o equations studied in previous papers by the authors are generalized to integral and integro-differential equations, and an abstract notion is also considered. New results are given on generic observability, and these results are then applied to give conditions under which that the minimal order of an equation equals the minimal possible dimension of a realization, just as with linear systems but in contrast to the discrete time nonlinear theory.

  13. E.D. Sontag and H.J. Sussmann. Nonlinear output feedback design for linear systems with saturating controls. In Proc. IEEE Conf. Decision and Control, Honolulu, Dec. 1990, IEEE Publications, 1990, pages 3414-3416, 1990. [PDF] Keyword(s): saturation, bounded inputs.
    This paper shows the existence of (nonlinear) smooth dynamic feedback stabilizers for linear time invariant systems under input constraints, assuming only that open-loop asymptotic controllability and detectability hold.

  14. E.D. Sontag. Nonlinear regulation, the piecewise linear approach. In Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1980, 1980. Keyword(s): piecewise linear systems.



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