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A Delay Partitioning Approach to Delay-Range-Dependent Stability Analysis of Fuzzy Systems

Min Kook Song, Jin Bae Park*, and Young Hoon Joo
International Journal of Control, Automation, and Systems, vol. 10, no. 1, pp.143-149, 2012

Abstract : This paper is concerned with the stability analysis of Takagi-Sugeno (T-S) fuzzy systems with time varying delays in a given range. The delay partitioning approach is proposed to solving the problem of stability analysis for T-S fuzzy systems. By employing a new type of Lyapunov-Krasovskii functionals, delay-range-dependent stability criteria are derived for T-S fuzzy systems. The idea of the approach is that the delay interval is uniformly divided into N segments with N a positive integer, and a proper Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functional. All the sufficient criteria are established in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI algorithm. Finally, numerical example is given to illustrate the less conservatism of the proposed method.

Keyword : Delay-decomposition, linear matrix inequalities, Takagi-Sugeno fuzzy systems, time-delay.

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