H∞ Fuzzy Filter Design for Nonlinear Sampled-Data Systems: An LMI Approach

In this paper, the problem of H^infin filtering design is studied for nonlinear sampled-data systems using the Takagi-Sugeno (T-S) fuzzy model approach. Traditionally, the sufficient conditions for the existence of such H^infin filter are characterized in terms of the solution of a differential Hamilton-Jacobi inequality with jumps, which is equivalent to solving the partial differential inequalities. There is no analytic solution for this nonlinear partial differential inequalities in general. First, in this study, the T-S fuzzy model is proposed to represent a class of nonlinear sampled-data systems. Next, using the T-S fuzzy model, the H^infin fuzzy filtering design problem for nonlinear sampled-data systems is characterized in terms of a linear matrix inequality problem (LMIP). Hence, the H^infin fuzzy filter of nonlinear sampled-data systems can be given via solving linear matrix inequalities (LMIs) instead of a differential Hamilton-Jacobi inequality with jumps.