Novel Delay-Dependent Stabilization Criterion for Lur’e Systems with Sector-Restricted Nonlinearities and External Disturbances via PD Feedback Approach

Chun Yin (), Shouming Zhong, Xiaoyun Liu and Zijian Liu
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Chun Yin: University of Electronic Science and Technology of China
Shouming Zhong: University of Electronic Science and Technology of China
Xiaoyun Liu: University of Electronic Science and Technology of China
Zijian Liu: University of Electronic Science and Technology of China

Journal of Optimization Theory and Applications, 2011, vol. 151, issue 1, No 6, 99 pages

Abstract: Abstract In this paper, the effects of time delay on control of Lur’e systems are considered. Using a convex representation of the nonlinearity, a novel delay-dependent stability criterion is derived for the Lur’e systems via proportional-derivative (PD) feedback law. The Lyapunov–Krasovskii functional based on the delay discretization approach is used for the purpose of obtaining the stability condition by utilizing Projection Lemma. The criterion is utilized to not only guarantee stability of systems but also reduce the effect of external disturbance to an norm constraint. Finally, two numerical examples show the effectiveness of the proposed method.

Keywords: Lur’e systems; stabilization; PD feedback controller; Linear matrix inequalities (LMIs); Convex optimization (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-011-9857-8

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