Global stabilization of cascade systems by C0 partial-state feedback

This paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization, and the notion and properties of the input-to-state stability Lyapunov function can be effectively coupled, resulting in globally stabilizing C/sup 0/ partial-state feedback controllers for a class of cascade systems which may not be smoothly stabilizable, even locally.

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

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

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

[4]  Eduardo Aranda-Bricaire,et al.  Constructive nonsmooth stabilization of triangular systems , 1999 .

[5]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[6]  Andrea Bacciotti,et al.  Local Stabilizability of Nonlinear Control Systems , 1991, Series on Advances in Mathematics for Applied Sciences.

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

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

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

[10]  Henry Hermes,et al.  Nilpotent and High-Order Approximations of Vector Field Systems , 1991, SIAM Rev..

[11]  Alberto Isidori,et al.  Nonlinear Control Systems II , 1999 .

[12]  J. Coron,et al.  Adding an integrator for the stabilization problem , 1991 .

[13]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

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

[15]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

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