Finite-time \(H_\infty\) control of periodic piecewise linear systems. (English) Zbl 1372.93097

Xie, Xiaochen; Lam, James; Li, Panshuo

Int. J. Syst. Sci., Princ. Appl. Syst. Integr. 48, No. 11, 2333-2344 (2017).

Summary: In this paper, the finite-time stability, stabilisation, \(L_2\)-gain and \(H_\infty\) control problems for a class of continuous-time periodic piecewise linear systems are addressed. By employing a time-varying control scheme in which the time interval of each subsystem constitutes a number of basic time segments, the finite-time controllers can be developed with periodically time-varying control gains. Based on a piecewise time-varying Lyapunov-like function, a sufficient condition of finite-time stability and the relevant time-varying controller are proposed. Considering the finite-time boundedness of the closed-loop periodic system, the \(L_2\)-gain criterion with continuous time-varying Lyapunov-like matrix function is studied. A finite-time \(H_\infty\) controller is proposed based on the \(L_2\)-gain analysis. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed criteria.

MSC:

93B36	\(H^\infty\)-control
93C05	Linear systems in control theory
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

finite-time stability; \(H_\infty\) control; \(L_2\)-gain; periodic piecewise systems