New Results on Nonsmooth Output Feedback Stabilization of Nonlinear Systems

This paper presents a nonsmooth output feedback framework for local and/or global stabilization of a class of inherently nonlinear systems, which may not be achieved by any smooth feedback controller. A systematic design algorithm is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but Holder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design procedure, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented fashion. Such nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems with unstabilizable/undetectable linearization. One of them is the global stabilizability of a chain of odd power integrators by Holder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a class of nonlinear systems studied in [14], where global stabilizability by nonsmooth state feedback was proved to be possible.

[1]  L. Rosier.  Homogeneous Lyapunov function for homogeneous continuous vector field , 1992 .

[2]  M. Kawski.  Stabilization of nonlinear systems in the plane , 1989 .

[3]  Wolfgang Hahn,et al.  Stability of Motion , 1967 .

[4]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[5]  W. P. Dayawansa,et al.  Recent Advances in The Stabilization Problem for Low Dimensional Systems , 1992 .

[6]  Wei Lin,et al.  Output feedback stabilization of a class of homogeneous and high-order nonlinear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[8]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[9]  I. Kolmanovsky,et al.  Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[10]  Wei Lin,et al.  Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization , 2001 .

[11]  W. P. Dayawansa,et al.  Asymptotic stabilization of a class of smooth two-dimensional systems , 1990 .

[12]  J. Tsinias,et al.  Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization , 1999 .

[13]  Wei Lin,et al.  On p-normal forms of nonlinear systems , 2003, IEEE Trans. Autom. Control..

[14]  Wei Lin,et al.  Nonsmooth output feedback stabilization of a class of genuinely nonlinear systems in the plane , 2003, IEEE Trans. Autom. Control..

[15]  Arthur J. Krener,et al.  Locally Convergent Nonlinear Observers , 2003, SIAM J. Control. Optim..

[16]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[17]  Wei Lin,et al.  Smooth output feedback stabilization of planar systems without controllable/observable linearization , 2002, IEEE Trans. Autom. Control..