Observers for stabilization of systems with matched uncertainty

In this article, we study the design of observer-based robust linear feedback controllers. The uncertainty, which can enterA, and either theB orC matrices, is assumed to satisfy certain matching conditions. Lyapunov techniques are used to establish sufficient conditions for stability, given an uncertainty bound. In particular, sufficient conditions are obtained that, if met, result in stabilizing controllers regardless of the size of the uncertainty entering the system matrix, as long as the standard constraints on the uncertainty entering the input or output matrices are met. As with the case of more general forms of uncertainty, the resulting observers often have high gains. To study performance, the problem of disturbance rejection is considered. Sufficient conditions are presented for obtaining control laws that stabilize the closed loop system, regardless of the size of the uncertainty entering the system matrix, while simultaneously guaranteeing arbitrarily small infinity norm for the transfer function from the plant disturbances to the outputs.

[1]  Faryar Jabbari,et al.  Robust linear controllers using observers , 1991 .

[2]  W. E. Schmitendorf,et al.  Stabilizing controllers for uncertain linear systems with additive disturbances , 1988 .

[3]  Min-Jea Tahk,et al.  Modeling of parameter variations and asymptotic LQG synthesis , 1987 .

[4]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[5]  B. Ross Barmish,et al.  Robustness of Luenberger Observers: Linear Systems Stabilized via Nonlinear Control , 1984, 1984 American Control Conference.

[6]  B. R. Barmish,et al.  The constrained Lyapunov problem and its application to robust output feedback stabilization , 1986 .

[7]  W. Perkins,et al.  Robust stabilization and disturbance rejection for systems with structured uncertainty , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[8]  George Leitmann,et al.  State feedback for uncertain dynamical systems , 1987 .

[9]  Lihua Xie,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1992 .

[10]  I. Petersen,et al.  High gain observers applied to problems in the stabilization of uncertain linear systems, disturbance attenuation and N∞ optimization , 1988 .

[11]  B. Barmish.  Necessary and sufficient conditions for quadratic stabilizability of an uncertain system , 1985 .

[12]  M. Corless,et al.  A new class of stabilizing controllers for uncertain dynamical systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[13]  B. Francis.  The optimal linear-quadratic time-invariant regulator with cheap control , 1979 .

[14]  L. Xie,et al.  Robust H^∞ Control for Linear Systems with Norm-Bounded Time-Varying Uncertainty , 1990 .

[15]  Ian R. Petersen.  A Riccati equation approach to the design of stabilizing controllers and observers for a class of uncertain linear systems , 1985 .

[16]  Hiroyuki Kano,et al.  Existence condition of positive-definite solutions for algebraic matrix riccati equations , 1987, Autom..

[17]  W. Schmitendorf,et al.  Effects of using Observers on Stabilization of Uncertain Linear Systems , 1991, 1991 American Control Conference.

[18]  Faryar Jabbari,et al.  A noniterative method for the design of linear robust controllers , 1990 .