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Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay. (English) Zbl 1082.93031
Summary: This paper considers the delay-dependent stability analysis and controller design for uncertain T-S fuzzy system with time-varying delay. A new method is provided by introducing some free-weighting matrices and employing the lower bound of time-varying delay. Based on the Lyapunov-Krasovskii functional method, sufficient condition for the asymptotical stability of the system is obtained. By constructing the Lyapunov-Krasovskii functional appropriately, we can avoid the supplementary requirement that the time-derivative of time-varying delay must be smaller than one. The fuzzy state feedback gain is derived through the numerical solution of a set of linear matrix inequalities (LMIs). The upper bound of time-delay can be obtained by using convex optimization such that the system can be stabilized for all time-delays. The efficiency of our method is demonstrated by two numerical examples.

##### MSC:
 93C42 Fuzzy control systems 93D05 Lyapunov and other classical stabilities of control systems
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##### References:
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