讨论了不确定时滞系统非脆弱控制器设计问题.利用Lyapunov-Krasovskii稳定性理论和最近建立的积分不等式方法,获得了不确定时滞系统在非脆弱控制器作用下不仅内部渐近稳定,而且具有给定的$H_{\mathrm{\infty }}$扰动抑制水平$\gamma$的时滞相关条件.然后,针对控制器具有加法不确定性和乘法不确定性两种情况,分别给出了非脆弱控制器的设计方法,这一方法不需要调节参数,利用Matlab的LMI工具箱求解方便,数值仿真实例说明该方法的有效性.

This paper is concerned with the problem of delay-dependent non-fragile Robust $H$-infinite control for uncertain systems. Based on an integral inequality method, a new delay-dependent condition, which can ensure that the closed-loop system is internally stable with a given $H$-infinite disturbance attenuation level via a non-fragile controller, is obtained by using the Lyapunov-Krasovskii stability theory. Then, the design of non-fragile $H$-infinite controller is proposed. No any parameter needs to be tuned. It can be easily solved in terms of linear matrix inequalities (LMI) in Matlab Toolbox. Finally, a numerical simulation is given to show the validity of this approach.