This paper deals with the $H_{\infty }$ control problem for a class of switched non-linear systems with structural uncertainty using robust passivity, even though the control problem for none of subsystems is solvable. Firstly, when each subsystem is only required to be robust passive in the associated active region, the $H_{\infty }$ control problem for such a system is solved by designing a state-dependent switching law and feedback controllers of subsystems. Secondly, when none of subsystems is robust passive, each subsystem is feedback equivalent to a robust passive system in the associated active region, and then solvability conditions of the $H_{\infty }$ control problem is obtained. Finally, two examples are presented to illustrate the effectiveness of the proposed design approach.

本文涉及 $H_{\infty }$一类具有鲁棒无源性的具有结构不确定性的切换非线性系统的控制问题，即使没有子系统的控制问题也可以解决。首先，当仅要求每个子系统在相关联的有源区域中具有鲁棒性时，$H_{\infty }$通过设计与状态相关的开关定律和子系统的反馈控制器，可以解决此类系统的控制问题。其次，当子系统中没有一个是鲁棒的无源系统时，每个子系统的反馈等效于相关联的有源区域中的一个鲁棒的无源系统，然后求解$H_{\infty }$获得控制问题。最后，给出两个例子来说明所提出的设计方法的有效性。