一类线性不确定切换系统的非脆弱控制器设计方法

Design Methods of Non-fragile Controllers for a Class of Uncertain Switched Linear Systems

针对一类线性不确定切换系统,在控制器增益存在加性摄动的情况下,给出了非脆弱状态反馈控制器的两种设计方案:方案1是利用多Lyapunov函数方法,通过子系统之间的切换,使系统对所有可允许的不确定性保持渐近稳定;方案2是基于平均驻留时间方法,给出了非脆弱状态反馈控制器存在的一个充分条件.相应的结果都是以线性矩阵不等式的形式给出.最后以一个数值例子说明了上述两种方法的有效性.

Two kinds of design schemes of non-fragile state-feedback controllers for a class of uncertain switched linear systems are developed. The controller gain to be designed is assumed to have additive gain variations. Based on multiple-Lyapunov function technique, the first design method guarantees that the switched system is asymptotically stable for all admissible uncertainties by means of switching among subsystems. The second method presents a sufficient condition for the existence of non-fragile controllers by employing average dwell time method. The corresponding results are all given in terms of linear matrix inequalities （LMIs）. Finally, a simulation example shows the effectiveness of the proposed approaches.