Robust stabilization of nonlinear systems by H ∞ state feedback

Abstract This paper is concerned with robust stabilization of nonlinear systems with unstructured uncertainty via state feedback. First, a robust stability condition is given for a closed loop system which is composed of a nonlinear nominal system and an unstructured uncertainty. Second, based on the obtained robust stability condition, a sufficient condition for robust stabilization by state feedback is given in terms of the solvability of some H ∞ state feedback control.

[1]  T. Yoshikawa,et al.  Bounded real Lemma of nonlinear systems and its application to H/sub /spl infin// state feedback control , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[2]  J. Willems.  The Generation of Lyapunov Functions for Input-Output Stable Systems , 1971 .

[3]  David J. Hill,et al.  Stability results for nonlinear feedback systems , 1977, Autom..

[4]  A. Schaft.  On a state space approach to nonlinear H ∞ control , 1991 .

[5]  T. Sugie,et al.  Global robust stabilization of nonlinear cascaded systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[6]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[7]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[8]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[9]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[10]  A. Isidori.  Feedback control of nonlinear systems , 1992 .

[11]  P. Moylan,et al.  Connections between finite-gain and asymptotic stability , 1980 .

[12]  Bonaventure Intercontinental,et al.  ON DECISION AND CONTROL , 1985 .

[13]  P. Moylan.  Implications of passivity in a class of nonlinear systems , 1974 .

[14]  M. Vidyasagar,et al.  New relationships between input-output and Lyapunov stability , 1982 .

[15]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .