一类不确定奇异多时滞系统的H_∞保成本控制

H∞Guaranteed Cost Control for Uncertain Singular Systems with Multiple Delays

针对一类具有多输入时滞并且范数有界的不确定参数的奇异系统,对鲁棒H∞保成本控制问题进行了研究.利用李亚普诺夫泛函和线性矩阵不等式(LMI)工具,首先给出了标称系统的鲁棒H∞保成本控制律存在的时滞依赖充分条件,然后将鲁棒保成本控制律的概念推广到具有多输入时滞的不确定奇异系统,并利用线性矩阵不等式可行解给出了控制律的设计方法和相应的性能指标上界.最后的仿真算例验证了该方法的有效性.

The problem of robust H∞ guaranteed cost control for a class of singular systems with multiple input delays and norm-bounded uncertain parameters is discussed. Based on Lyapunov functional and linear matrix inequality （LMI） approach, a delay-dependent sufficient condition for the existence of robust H∞ guaranteed cost controller for the nominal system is presented. Moreover, the concept of robust H∞ guaranteed cost controller is extended to uncertain singular systems with multiple input delays. The design approaches of the controller and the upper boundary of the performance index are given by means of the feasible solutions of LMIs. Finally, an illustrative example is given to show the effectiveness of the proposed method.