中文摘要：

在研究一类区间时变时滞线性系统稳定性的基础上,针对一类时变时滞线性切换系统状态反馈的H∞控制问题,研究了系统的鲁棒H∞控制器的设计问题,利用多Lyapunov函数方法定义了更为一般的Lyapunov函数,通过使用倒数凸组合的方法得到了系统在切换规则下达到鲁棒镇定且满足H∞的充分条件,以及系统的鲁棒H∞控制器存在的充分条件。此条件充分考虑到时滞上下界的信息,使得到的结果具有更小的保守性。与此同时,在计算Lyapunov函数的导数时使用Jensen积分不等式的放缩方法和线性矩阵不等式的方法,同样降低了保守型。最后,使用线性变换降低了计算的复杂程度。为了方便利用Matlab工具箱求解线性矩阵不等式,将最终得到的充分条件转化成线性矩阵不等式的形式表示。

英文摘要：

On the basis of studying the stability of time-varying delay linear systems,which is a differentiable function for a given interval,and aiming at the control problem for a class of switched time-varying delay linear systems,this paper considers the designing issue of H_∞ robust controllers for a system,a more general Lyapunov function is defined by multiple Lyapunov function method,and through reciprocally convex approach,sufficient conditions are obtained,which make the system reaches robust stabilization,meet H∞ Performance Bound and ensure the existence of the controllers,these conditions sufficiently consider the upper and lower bound of delay,make the developed results have less conservatism,at the same time,As the same time,Jensen integral inequality approach and linear matrix inequality（LMI）are employed so as to get a less conservative result,when the derivative of Lyapunov function is calculated,finally,linear transformation is used to reduce the calculating complexity.For convenience,Matlab toolbox is utilized to solve linear inequalities so as to express the sufficient conditions got at last with the form of linear matrix inequality（LMI）.