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.

本文利用线性积分型Lyapunov–Krasovskii泛函（LKF）来处理Itô随机延迟IT2模糊系统的随机渐近稳定性分析和扩展耗散性问题以及控制器设计。很好地估计了线积分型LKF的上限，在此基础上，得出了随机渐近稳定性和扩展耗散性的条件。在数值示例中，对线积分类型LKF和二次LKF导出的条件进行了比较，以表明线积分方法的条件比通过二次方法的条件更普遍。同时，这些条件对于某些矩阵变量而言是非线性形式，这使得确定扩展耗散控制器变得困难。受锥互补线性化算法和新颖的矩阵解耦方法的启发，通过将非线性矩阵不等式转化为具有线性矩阵不等式约束的二次优化问题，开发了状态反馈控制器。最后，给出两个例子来说明我们提出的方法的有效性。