Robust <i>H</i><sub>∞</sub> Control for Uncertain Singular Perturbed Systems With Time Delay

WANG Yanyan; LIU Wei; WANG Zhiming

doi:10.11936/bjutxb2014090003

Journal of Beijing University of Technology > 2016 > 42(2): 217-222. > DOI: 10.11936/bjutxb2014090003

WANG Yanyan, LIU Wei, WANG Zhiming. Robust H_∞ Control for Uncertain Singular Perturbed Systems With Time Delay[J]. Journal of Beijing University of Technology, 2016, 42(2): 217-222. DOI: 10.11936/bjutxb2014090003

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Robust H_∞ Control for Uncertain Singular Perturbed Systems With Time Delay

1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, Henan, China;
2. Department of Mathematics, East China Normal University, Shanghai 200241, China

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Received Date: August 31, 2014
Available Online: January 10, 2023

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Abstract

This paper studies the robust H_∞ control problem for a class of uncertain singularly perturbed systems with state delay.Based on linear matrix inequalities and Lyapunov method,a sufficient condition for asymptotic stability of the closed-loop systems is derived,in which the criterion presented is independent of the small parameter.Meanwhile,the controller is designed.In addition,the upper bound for the systems with the given H_∞ performance is obtained by solving a generalized eigenvalue problem(GEVP).Finally,two numerical examples are presented to illustrate the effectiveness of the proposed method.
- singularly perturbed systems,
- robust control,
- linear matrix inequality(LMI),
- H_∞ control

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Robust H_∞ Control for Uncertain Singular Perturbed Systems With Time Delay