$H_{\infty} $ Filter Design for Nonlinear Systems With Time-Delay Through T–S Fuzzy Model Approach

This paper is concerned with the $H_{\infty} $ filter design for nonlinear systems with time-varying delay via Takagi–Sugeno fuzzy model approach. Delay-dependent design method is proposed in terms of linear matrix inequalities (LMIs), which forms the main contribution of this paper. The main technique used is the free-weighting matrix method combined with a matrix decoupling approach. The results for rate-independent case, delay-independent case, and delay-free case are also given as easy corollaries. An illustrative example is given to show the effectiveness of the present method.