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Exponential stability of filtering problems for delay fuzzy systems

This paper concerns fuzzy filter design problems for a continuous-time T-S fuzzy system with multiple time delays in the state variables. By using a standard quadratic Lyapunov function, globally exponential stability is demonstrated for the filtering error fuzzy system. And due to the simplest structure of Lyapunov function, the bounds and varying rates of delay times are unknown in this work. A sufficient condition is stated in terms of LMI, which can be solved easily by existing convex algorithms. Lastly, an example illustrates the proposed design methodology.