一类不确定线性切换系统的鲁棒镇定

研究了一类不确定线性切换系统基于状态反馈的鲁棒镇定问题.此类切换系统不仅具有未知时变但有界的结构不确定性,还具有不满足匹配条件的外部扰动.首先利用完备性条件与共同李亚谱诺夫函数方法,在各子系统不需满足镇定的条件下,设计了切换系统的状态反馈鲁棒控制器及相应的切换策略,使不确定线性切换系统的状态在其平衡点处渐近稳定,得到了切换系统可状态反馈镇定的充分条件;然后基于凸组合技术与线性矩阵不等式方法,将所得结果用易于求解的线性矩阵不等式的形式表出;最后通过仿真例子表明所设计的状态反馈控制器在给定的切换策略下,可使不确定切换系统的状态达到渐近稳定.

Robust Stabilization for a Class of Uncertain Switched Linear Systems

The problem of robust stabilization based on state feedback for a class of uncertain switched linear systems is studied. The switched systems not only exist unknown time-varying but norm-bounded uncertainty in structure, but also exist outside disturbance which does not satisfy so-called matching condition. Firstly by using completeness condition and the common Lyapunov function method,the state feedback robust controllers and the switching law were designed to guarantee the states of the systems asymptotitally stable on the equilibrium point on condition that each subsystem can not be stabilized. And the sufficient condition of robust stabilization for switched systems is obtained. Secondly based on convex combinations technique and linear matrix inequalities method, the result is expressed in the form of linear matrix inequalities,which can be solved easily. Finally the simulation shows that the designed controller can make the states of the switched systems asymptotically stable under the given switching law.