中文摘要：

研究控制器增益存在加性摄动时的一类线切换系统的非脆弱鲁棒H∞控制问题.首先,利用多Lyapunov函数方法,把状态空间划分为N（子系统个数）个子区域,并以最小Lyapunov函数作为切换规则,研究标称系统的稳定性,而给出的稳定性条件不要求每一个子系统都是渐近稳定的.然后,考虑系统的不确定性,给出了非脆弱状态反馈控制器和切换律设计方案.通过子系统之间的切换,保证系统对所有允许的不确定性是渐近稳定的且具有H∞性能界,并以线性矩阵不等式组的形式给出控制器增益矩阵存在的充分条件.最后,以数值仿真验证了该方法的有效性.

英文摘要：

The non-fragile robust H∞ control problem is studied for a class of switched linear systems w ith additional controller gain variations.First,based on the multiple Lyapunov functions method,the state space is partitioned into N（the number of subsystems） regions,and the minimum Lyapunov function is considered as the sw itching law.The stability of the nominal system of the linear sw itched system is studied,and the given stability conditions do not require that every subsystem is asymptotically stable.Then,considering the uncertainties in the system,a design scheme is presented to the non-fragile state feedback controllers and their sw itching law s.By the sw itching among the subsystems,the sw itched system is globally asymptotically stable w ith H∞-norm bound for all the admissible uncertainties.The existing conditions of controller gain matrices are given in the term of linear matrix inequalities.Finally,a simulation example is given to demonstrate the effectiveness of the proposed design procedure.