一类变时滞不确定切换系统的鲁棒控制器设计

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.

Robust Controllers Design for a Class of Uncertain Switched Systems with Time-varying Delay

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 other does not satisfy matching condition. Under the assumption that each subsystem can not be stabilized,by using 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 inequality. 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.