Stability conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach

C. Lin; Q.-G. Wang; T.H. Lee; Y. He

Stability conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach

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Stability conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach

Author(s): C. Lin ; Q.-G. Wang ; T.H. Lee ; Y. He
DOI: 10.1049/iet-cta:20050165

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Author(s): C. Lin ¹ ; Q.-G. Wang ² ; T.H. Lee ² ; Y. He ²
- Affiliations: 1: Institute of Complexity Science, Qingdao University, Qingdao, People's Republic of China
  2: Department of Electrical and Computer Engineering, National University of Singapore, Singapore
Source: Volume 1, Issue 1, January 2007, p. 127 – 132
DOI: 10.1049/iet-cta:20050165 , Print ISSN 1751-8644, Online ISSN 1751-8652

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The asymptotic stability of Takagi–Sugeno (T–S) fuzzy systems with state delay is studied. The aim is not only to extend the fuzzy weighting-dependent Lyapunov function method for delay-free fuzzy systems to time-delay fuzzy systems, but also to provide state-of-the-art stability analysis methods for time-delay fuzzy systems. First, the fuzzy weighting-dependent Lyapunov–Krasovskii functional is used to reduce the conservatism entailed in previous results using quadratic Lyapunov–Krasovskii functionals. By adopting a recent technique called the free-weighting matrix method, a delay-dependent stability condition that improves existing results for time-delay fuzzy systems is derived. Next, an augmented fuzzy weighting-dependent Lyapunov–Krasovskii functional is proposed to further reduce the conservatism. Delay-independent stability criteria are easy corollaries of the present delay-dependent results. Finally, three examples are given to illustrate the reduced conservativeness achieved by the proposed methods.

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Stability conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach

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