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

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
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