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Journal of Vibration and Control
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LMI-based Approach of Global Exponential Robust Stability for a Class of Uncertain Distributed Parameter Control Systems with Time-varying Delays

Linshan Wang

Department of Mathematics, Ocean University of China, Qingdao, 266071 China, and Department of Mathematics, Liaocheng University, Liaocheng, 252059 China, wils115cn{at}yahoo.com.cn

Yangfan Wang

College of Communication Engineering, Ocean University of China, Qingdao, 266071 China

In this paper, the global exponential robust stability analysis problem is considered for a class of uncertain distributed parameter control systems with time-varying delays. The uncertain parameters are generated from modeling errors as well as parameter variations in the systems. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the uncertain system is globally exponentially robustly stable. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions and therefore global exponential robust stability for the uncertain distributed parameter control systems with time-varying delays can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.

Key Words: Distributed parameter systems • time-varying delay • uncertain parameters • robust control • linear matrix inequality • global exponential robust stability.

This version was published on August 1, 2009

Journal of Vibration and Control, Vol. 15, No. 8, 1173-1185 (2009)
DOI: 10.1177/1077546307082926
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