一类变时滞不确定切换系统的鲁棒控制器设计

Design of robust controllers for a class of uncertain switched systems with time-varying delay

基于线性矩阵不等式方法和凸组合技术,研究了一类具有范数有界不确定性的切换系统的状态反馈控制问题.系统的状态时滞是时变的,外部非线性扰动分解成满足匹配条件和不满足匹配条件两部分.在每个子系统均不能镇定的情况下,利用单Lyapunov函数方法和多Lyapunov函数方法,分别得到了此类系统鲁棒可稳的充分条件,并相应的转化为求解线性矩阵不等式问题.进而设计出鲁棒控制器和相应的切换策略,保证闭环系统是渐近稳定的.最后,通过数值算例说明了本文所设计方法的正确有效性.

Based on linear matrix inequality （LMI） method and convex combination technique, the problem of state feedback control for switched systems with norm - bounded uncertainties is studied. State delay is time - varying. Nonlinear disturbance is decomposed into two parts, one part satisfies matching condition and the oth- er does not satisfy matching condition. Under the assumption that each subsystem can not be stabilized, by u- sing single Lyapunov function technique and multiple Lyapunov function technique, a sufficient condition of robust stabilization for switched systems is obtained and expressed as a problem of solving linear matrix ine- quality. Robust controllers and corresponding switching laws are designed to guarantee the closed-loop systems to be asymptotically stable. A numerical example shows the validity of the design method.