时变时滞奇异脉冲切换系统的鲁棒弹性保成本控制

Robust Resilient Guaranteed Cost Control for Singular Impulsive Switched Systems with Time-varying Delay

关键词:  奇异切换系统  脉冲切换系统  弹性保成本控制  多Lyapunov技术  线性矩阵不等式

Key words:  singular switched systems  impulsive switched systems  resilient guaranteed cost control  multiple Lyapunov technique  linear matrix inequalities (LMIs)

摘要:

针对一类具有时变时滞的奇异脉冲切换系统,研究鲁棒弹性保成本控制问题.首先,基于多Lyapunov泛函技术,建立标称自由系统具有正则性、因果性及渐近稳定性的充分条件.然后,给出一个弹性保性能控制器的设计方案,该方案能保证对所有容许的不确定性,闭环系统是正则的、因果的和渐近稳定的,且成本函数不超过某个上界.并进一步运用矩阵最大奇异值的最小化方法和凸优化方法,求解最优鲁棒弹性保成本控制器.所有的充分条件均巧妙地表示为线性矩阵不等式形式.最后,运用两个仿真实例验证本研究方法较少的保守性和有效性.

Abstract:

This paper focuses on the problem of robust resilient guaranteed cost control for a class of singular impulsive switched systems with time-varying delay.Based on the multiple Lyapunov functional technique,some sufficient criteria,ensuring the regularity,causality,and asymptotic stability,are obtained initially for the nominal and unforced systems.Then the resilient controller is designed such that the corresponding closed-loop system,for all admissible uncertainties,is regular,causal and asymptotically stable, and the cost function does not exceed a cost upper bound.Further,a minimization approach of the largest singular value of matrices and a convex optimization method are introduced to seek the optimal robust resilient guaranteed cost controller.All the conditions are cast into the form of linear matrix inequalities (LMIs) through ingenious processing.Finally,two examples are presented to illustrate the less conservativeness and the effectiveness of the proposed results.