Laboratory for Control, Learning, and Systems Biology

Papers by Y. Lin and E.D. Sontag

1996
  1. ▪Y. Lin, E.D. Sontag, Y. Wang, "A smooth converse Lyapunov theorem for robust stability", SIAM J. Control Optim., vol. 34, no. 1, pp. 124–160, 1996. doipdf
    input to state stability
    Abstract

    This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets.

1995
  1. ▪Y. Lin, E.D. Sontag, "Control-Lyapunov universal formulas for restricted inputs", Control Theory and Advanced Technology, vol. 10, no. 4, part 5, pp. 1981–2004, 1995. pdf
    control-Lyapunov functions · saturation · bounded inputs
    Abstract

    We deal with the question of obtaining explicit feedback control laws that stabilize a nonlinear system, under the assumption that a "control Lyapunov function" is known. In previous work, the case of unbounded controls was considered. Here we obtain results for bounded and/or positive controls. We also provide some simple preliminary remarks regarding a set stability version of the problem and a version for systems subject to disturbances.

  2. ▪Y. Lin, E.D. Sontag, Y. Wang, "Input to state stabilizability for parametrized families of systems", Internat. J. Robust Nonlinear Control, vol. 5, no. 3, pp. 187–205, 1995. pdf
    ISS · stabilization
    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.

1994
  1. ▪Y. Lin, E.D. Sontag, "On control-Lyapunov functions under input constraints", In Proc.\ IEEE Conf.\ Decision and Control, Orlando, Dec.\ 1994, IEEE Publications, 1994, pp. 640–645, 1994.
    control-Lyapunov functions
  2. ▪Y. Lin, E.D. Sontag, Y. Wang, "Recent results on Lyapunov-theoretic techniques for nonlinear stability", In Proc.\ Amer.\ Automatic Control Conf., Baltimore, June 1994\/, pp. 1771–1775, 1994.
1993
  1. ▪Y. Lin, E.D. Sontag, Y. Wang, "Lyapunov-function characterizations of stability and stabilization for parameterized families of systems", In Proc.\ IEEE Conf.\ Decision and Control, San Antonio, Dec.\ 1993, IEEE Publications, 1993, pp. 1978–1983, 1993.
1992
  1. ▪Y. Lin, E.D. Sontag, "Gradient techniques for steering systems with no drift", In Proc.\ Conf.\ Inform.\ Sci.\ and Systems, Princeton University, March 1992, pp. 1003–1008, 1992.
  2. ▪E.D. Sontag, Y. Lin, "Stabilization with respect to noncompact sets: Lyapunov characterizations and effect of bounded inputs", In Nonlinear Control Systems Design 1992, IFAC Symposia Series, M.\ Fliess Ed., Pergamon Press, Oxford, 1993, pp. 43–49, 1992. pdf
    Also in Proc.\ Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M.\ Fliess, Ed.), IFAC Publications, pp. 9–14
    saturation · bounded inputs
1991
  1. ▪Y. Lin, E.D. Sontag, "A universal formula for stabilization with bounded controls", Systems Control Lett., vol. 16, no. 6, pp. 393–397, 1991. doipdf
    stabilization · nonlinear systems · saturation · bounded inputs · control-Lyapunov functions · real-analytic functions
    Abstract

    We provide a formula for a stabilizing feedback law using a bounded control, under the assumption that an appropriate control-Lyapunov function is known. Such a feedback, smooth away from the origin and continuous everywhere, is known to exist via Artstein's Theorem. As in the unbounded-control case treated in a previous note, we provide an explicit and ``universal'' formula given by an algebraic function of Lie derivatives. In particular, we extend to the bounded case the result that the feedback can be chosen analytic if the Lyapunov function and the vector fields defining the system are analytic.

  2. ▪Y. Lin, E.D. Sontag, "Further universal formulas for Lyapunov approaches to nonlinear stabilization", In Proc.\ Conf.\ Inform.\ Sci.\ and Systems, John Hopkins University, March 1991, pp. 541–546, 1991.