H2 and H∞ fuzzy filters with memory for Takagi-Sugeno discrete-time systems

Abstract This paper is concerned with the problem of H 2 and H ∞ fuzzy filter design for Takagi–Sugeno (T–S) discrete-time systems. The novelty of the proposed method, in the context of T–S fuzzy systems, is the inclusion of an arbitrary number of past information (states and measurements) in the structure of the filter, producing a T–S fuzzy filter with memory. Linear matrix inequality relaxations based on multi-polynomial fuzzy Lyapunov functions are proposed for the filter design, providing filters that attain lower bounds for the H 2 and H ∞ performance criteria, when compared to other approaches available in the fuzzy literature that employ memoryless filters. The advantages of the proposed approach are illustrated by numerical examples.

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