改进的不确定时滞系统时滞相关鲁棒镇定结论

针对一类不确定时滞系统,研究了其时滞相关鲁棒镇定问题.通过将整个时滞区间划分为许多子区间,并在每个子区间上定义不同的能量函数,定义了一种新的Lyapunov-Krasovskii泛函.基于此泛函,并借助线性矩阵不等式工具,给出了标称时滞系统的时滞相关稳定条件.基于得到的稳定条件给出了状态反馈控制器的设计方法,得到的控制律可保证相应的闭环系统鲁棒渐近稳定.最后,仿真示例表明了该方法的可行性.

Improved Delay-Dependent Robust Stabilization Result for Uncertain Systems with Time-Delay

The problem of delay-dependent robust stabilization for uncertain systems with time-delay is considered.A Lyapunov-Krasovskii functional is designed by splitting the whole time-delay interval into some subintervals and defining different energy functions in every subinterval.Using the linear matrix inequality technique,a delay-dependent stability criterion is derived to ensure the nominal system to be stable.Based on the criterion,the problem is solved via a state feedback controller,guaranteeing the resultant closed-loop system to be robustly asymptotically stable.Finally,a numerical example is given to illustrate the effectiveness of the proposed method.