带非线性扰动多时滞系统的鲁棒稳定

Robust Stability of Multiple Time-delay Systems with Nonlinear Perturbations

研究一类带有非线性扰动的不确定多时滞系统的鲁棒稳定问题.基于李雅普诺夫定理,给出了系统多时滞相关的稳定准则,再通过对闭环系统进行稳定分析,推导出状态反馈控制的充分条件,该条件进一步等价地转化为一系列线性矩阵不等式的可解性问题.通过两个例子说明文中所提出的方法可减少结果的保守性,证明文中鲁棒控制方法的有效性.

The problem with robust stabilization of uncertain multiple time-delay systems with nonlinear perturbation is proposed. Firstly, based on Lyapunov stability theory, the delay dependent stabilization criteria for the system are set. Secondly, robust controller is given by analyzing the stability of class-loop system. The sufficient condition for the existence of the state feedback controller is derived in terms of linear matrix inequalities. It is finally illustrated that the method presented can reduce the conservativeness of the results, which indicates the validity of the proposed method.