Dissipative filtering for discrete fuzzy systems

The goal of this paper is, via dissipative theory, to design a dissipative filter for a class of nonlinear systems described by Takagi-Sugeno (TS) fuzzy model. We first reformulate the problems in an estimation/filtering error system such that the error system is dissipatively asymptotically stable with respect to a specifically chosen quadratic supply rate. Then we derive the synthesis conditions based on Lyapunov method, leading to an LMI representation that can be numerically solved by existing LMI solvers. We demonstrate that a class of filtering problems can be formulated into a general quadratic dissipative framework. Finally the utility of the proposed method is illuminated by an example.