H∞ Filter for Discrete-Time Takagi-Sugeno Fuzzy Systems with Time-Varying Delays via a Novel Wirtinger-Based Inequality

This paper is devoted to the analysis and design of H-infinity filtering for discrete-time Takagi-Sugeno (TS) fuzzy systems with time-varying delays. By using the delay-partitioning method, more systematic information is introduced, which can reduce the conservatism of the conclusion. By constructing an appropriate Lyapunov functional and combining with a newly Wirtinger-based summation inequality, the existence condition of the H-infinity filter is obtained. Thus, utilizing the contract matrix transformation method, the H-infinity filter design for discrete-time TS fuzzy systems with time-varying delay based on LMI is proposed. Finally, a few numerical analysis results are given to prove the effectiveness of the method.