多状态时变时滞线性切换系统的鲁棒二次镇定H∞控制

摘要

This paper addresses the problem of robust quadratic stabilization H∞ control for a class of linear switched systems with uncertain multiple time-varying delays in state and input based on LMI and H∞ theory. Based on multiple Lyapunov function techniques and by constructing linear matrix inequalities, several sufficient conditions for the problem to be solvable are derived by using a state-based switching law. Meanwhile, robust H∞ controllers for each subsystem and switching law are designed. A numerical example shows effectiveness of the method.%基于LMI和H∞控制理论,研究了一类具有不确定和时滞的线性切换系统的鲁棒二次镇定H∞控制问题.利用多Lyapunov函数技术构造线性矩阵不等式,在基于状态的切换规则下,给出了这类系统鲁棒二次镇定且具有H∞性能界的充分条件,以及切换规则和鲁棒H∞切换控制器的设计方案.最后用数值例子对所得结果加以验证,表明了文中给出结果的有效性.