Performance analysis and extended dissipative controller design for Itô stochastic-delayed IT2 fuzzy models

Abstract

This paper deals with the problems of stochastic asymptotic stability analysis and extended dissipativity as well as controller design for Itô stochastic-delayed IT2 fuzzy systems by using line integral type Lyapunov–Krasovskii functional (LKF). A good estimate of the upper bound for the line integral type LKF is achieved, based on which, the conditions of stochastic asymptotic stability and extended dissipativity are derived. A comparison has been drawn between the conditions derived by line integral type LKF and the ones by the quadratic LKF in a numerical example, to indicate that the conditions by line integral approach are more general than the ones via quadratic method. Meanwhile, these conditions are of nonlinear form with respect to some matrix variables which makes the determination of the extended dissipative controller difficult. Inspired by cone complementarity linearisation algorithm and a novel matrix decoupling method, the state feedback controller is developed by transforming the nonlinear matrix inequalities into a quadratic optimisation problem with linear matrix inequality constraints. Finally, two examples are given to show the validity of our proposed approach.