Finite-time control of periodic piecewise linear systems

Xiaochen Xie, James Lam and Panshuo Li

International Journal of Systems Science, 2017, vol. 48, issue 11, 2333-2344

Abstract: In this paper, the finite-time stability, stabilisation, L2-gain and H∞ 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 L2-gain criterion with continuous time-varying Lyapunov-like matrix function is studied. A finite-time H∞ controller is proposed based on the L2-gain analysis. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed criteria.

Date: 2017
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DOI: 10.1080/00207721.2017.1316884

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