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Publications about 'integral input to state stability'
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. 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.


  3. 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.


  4. 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.


  5. 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.


  6. 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.


  7. 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.


  8. 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.


  9. 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.


  10. 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.


  11. 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.


Conference articles
  1. B.P. Ingalls, E.D. Sontag, and Y. Wang. Remarks on input to output stability. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 1226-1231, 1999. Keyword(s): input to state stability, integral input to state stability, input to output stability.


  2. 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.


  3. D. Angeli, E.D. Sontag, and Y. Wang. A remark on integral input to state stability. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 2491-2496, 1998. Keyword(s): input to state stability.


  4. 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.



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