H∞ control problem of linear periodic piecewise time-delay systems

Xiaochen Xie, James Lam and Panshuo Li

International Journal of Systems Science, 2018, vol. 49, issue 5, 997-1011

Abstract: This paper investigates the H∞ control problem based on exponential stability and weighted L2-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov–Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and L2-gain analyses, sufficient delay-dependent exponential stability and weighted L2-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an H∞ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.

Date: 2018
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DOI: 10.1080/00207721.2018.1440028

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