Line Integral Approach to Extended Dissipative Filtering for Interval Type-2 Fuzzy Systems

Abstract

This article is concerned with the problems of extended dissipativity analysis and filter design for interval type-2 (IT2) fuzzy systems. Based on the line integral Lyapunov function, a sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration is established. A LMI-based equivalent condition to the obtained one in a nonlinear form is provided by combining congruence transformation with change of variables. This LMI condition obtained is more general than the one which is based on the common quadratic Lyapunov function. Meanwhile, in terms of parameterization, the extended dissipative filter is developed which guarantees the asymptotic stability and extended dissipativity for the filtering error system. Furthermore, our filter obtained by the parameterization method includes the one obtained by the equivalent transformation method as a special case. Two simulation examples are provided to show the merits and effectiveness of the proposed approach.