Extended Dissipativity and Control Synthesis of Interval Type-2 Fuzzy Systems via Line-Integral Lyapunov Function

Abstract

This article addresses the problems of the stability and extended dissipativity analysis and control synthesis for interval type-2 fuzzy systems. A sufficient condition of asymptotic stability and extended dissipativity of the systems under consideration is established by using line-integral Lyapunov function. This condition obtained is more general than the one which is based on quadratic Lyapunov function. Calculating the control gains in light of the obtained condition is more complicated and challenging, since the matrix inequalities in the condition are of nonlinear form with respect to some matrix variables. Also, change of variable as well as the existing matrix decoupling approach cannot be used directly to handle the nonlinear problem. By utilizing cone complementarity linearization algorithm and a new matrix decoupling method, the state feedback controller can be developed by converting the nonlinear matrix inequalities into a quadratic optimization problem with linear inequality constraints. Four simulation examples are provided to show the effectiveness of the proposed approach.