不确定时滞系统的鲁棒绝对稳定性研究

On the robust absolute stability of uncertain time-delay systems

基于Lyapunov稳定性理论,采用线性矩阵不等式处理方法,研究具有参数不确定性的时滞系统鲁棒绝对稳定性问题.导出了用线性矩阵不等式系统可行性描述的系统鲁棒绝对稳定的滞后依赖型条件,据此可计算出最大的允许时滞界.通过求解一组线性矩阵不等式,给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律设计方法.

The problem of robust absolute stability is studied for a class of uncertain time-delay systems based on Lyapunov stability theory. A delay-dependent sufficient condition for the robust absolute stability is derived and is expressed as the feasibility problem of a certain linear matrix inequality system. And a maximum delay bound is obtained by solving a corresponding convex optimization problem. Furthermore, a procedure of designing memoryless state feedback controllers is presented such that the closed-loop uncertain systems are robustly absolutely stable.