A New H_∞Filter Design For Nonlinear Systems With Time-varying Delays Based On T-S Fuzzy Model

With the development of modern industry, nowadays most systems are nonlinear anduncertain. These characteristics promote the development of fuzzy control and H_∞filtering.Based on the T-S fuzzy model, this paper study the filter design for nonlinear systems withtime-delay by adopting appropriate Lyapunov-Krasovskii functional, using linear matrixinequality and Schur complement. The main results are as follows:1. A new design method of H_∞filter is proposed based on the T-S fuzzy model for nonlinearsystems with time-delay. Firstly, the sufficient condition of the existence of H_∞filter is givedby adopting a new Lyapunov-Krasovskii functional with triangle integral. Eventually, a newdesign method of H_∞filter is proposed by matrix decoupling and the convex combination. Themethod guarantees the filtering error system is not only asymptotically stable, but also satisfiesH_∞performance index under zero initial condition.2. On the basis of1, a new design method of robust H_∞filter is proposed for uncertainnonlinear systems with time-delay.