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Publications of Eduardo D. Sontag jointly with D. Liberzon
Articles in journal or book chapters
  1. J.P. Hespanha, D. Liberzon, D. Angeli, and E.D. Sontag. Nonlinear norm-observability notions and stability of switched systems. IEEE Trans. Automat. Control, 50(2):154-168, 2005. [PDF] Keyword(s): observability, input to state stability, observability, invariance principle.
    Abstract:
    This paper proposes several definitions of observability for nonlinear systems and explores relationships among them. These observability properties involve the existence of a bound on the norm of the state in terms of the norms of the output and the input on some time interval. A Lyapunov-like sufficient condition for observability is also obtained. As an application, we prove several variants of LaSalle's stability theorem for switched nonlinear systems. These results are demonstrated to be useful for control design in the presence of switching as well as for developing stability results of Popov type for switched feedback systems.


  2. 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, 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.


  3. 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, 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.


Conference articles
  1. J.P. Hespanha, D. Liberzon, and E.D. Sontag. Nonlinear observability and an invariance principle for switched systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 4300-4305, 2002. [PDF] Keyword(s): observability.


  2. D. Liberzon, A.S. Morse, and E.D. Sontag. Output-input stability: a new variant of the minimum-phase property for nonlinear systems. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 743-748, 2001. Keyword(s): input to state stability.


  3. D. Liberzon, A.S. Morse, and E.D. Sontag. A new definition of the minimum-phase property for nonlinear systems, with an application to adaptive control. In Proc. IEEE Conf. Decision and Control, Sydney, Dec. 2000, IEEE Publications, 2000, pages 2106-2111, 2000.


  4. 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, 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.



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Last modified: Thu Nov 23 10:40:56 2017
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