一类不确定切换奇异时滞系统的时滞依赖鲁棒镇定

针对一类不确定切换奇异时滞系统,对其鲁棒镇定问题进行了研究.首先利用多李亚普诺夫泛函方法和线性矩阵不等式工具,通过引入适当的自由权矩阵,在适当的切换律下,给出了基于严格线性矩阵不等式表示的标称自治切换奇异系统正则、无脉冲且渐近稳定的时滞依赖条件;然后基于此条件,通过设计相应的状态反馈子控制器,得到了保证闭环系统对所有允许的不确定性是正则、无脉冲且渐近稳定的时滞依赖条件,同时给出了子控制器的显示表达式.数值算例表明该方法的有效性.

Delay-dependent Robust Stabilization for a Class of Uncertain Switched Singular Systems with Time-delay

The problem of robust stabilization for a class of uncertain switched singular systems with time-delay is considered.Firstly,by means of the multiple Lyapunov functional method and linear matrix inequality(LMI) tools and by introducing some appropriate free-weighting matrices,a delay-dependent stability criterion is given to ensure that the nominal unforced switched singular system is regular,impulse free and asymptotically stable under an appropriate switching law in terms of strict LMIs.Then,based on the criterion,a delay-dependent sufficient condition is deduced by designing state feedback sub-controllers,such that the resultant closed-loop systems are regular,impulse free and asymptotically stable for all admissible uncertainties.An explicit expression for the designed sub-controllers is also given.Numerical examples show that the results obtained are effective.