具有变时滞的非线性系统的时滞相关非脆弱保成本控制

Delay-Dependent Nonfragile Guaranteed Cost Control for Nonlinear Systems with Time-Varying Delays

对于一类具有变时滞和控制器增益摄动的非线性系统,研究非脆弱保成本控制问题。在控制器参数存在加法摄动和乘法摄动2种情况下,设计1个无记忆状态反馈非脆弱保成本控制律,使闭环系统渐近稳定,并且闭环性能指标不超过某个确定的上界。利用线性矩阵不等式方法,给出时滞相关的非脆弱保成本控制律存在的条件和控制器的设计方法。

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear systems with time-varying delays and controller gain perturbations. Aguaranteed cost control law is designed under two classes of perturbations, namely, additive perturbations and multiplicative perturbotions, which is a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality （LMI） approach, some delay-dependent conditions for the existence of such controllers are derived. A numerical example is given to illustrate the proposed method.