具有多个时滞的积分时滞系统的稳定性分析

首先,针对具有多个时滞的积分时滞系统,建立新的基于线性矩阵不等式的稳定性条件.该条件与正整数k有关,给出$k=1$时该条件与现有结果间的关系.该关系表明所提出条件在$k\geqslant2$时的保守性比现有结果小;然后,基于所提出的稳定性条件,进一步研究具有参数不确定性的积分时滞系统的鲁棒稳定性问题,建立基于线性矩阵不等式的充分条件;最后,利用所提出方法,研究具有多个离散时滞和分布时滞的积分时滞系统的稳定性问题.数值算例结果表明了所提出稳定性判据的有效性.

Stability analysis of integral delays systems with multiple time-delays

This paper investigates the stability analysis of integral delay systems with multiple delays. A new stability condition in terms of linear matrix inequalities (LMIs) indexed by a positive integer k is provided. When $k=1$, the relationship between this condition and an existing result is revealed, which shows that the proposed condition with $k\geqslant2$ can be less conservative than the existing ones. Based on the proposed stability condition, the robust stability problem for perturbed integral delay systems is investigated, and the results are expressed using LMIs. By using the proposed method, the stability analysis of integral time-delay systems with multiple discrete and distributed time delays are studied. Numerical examples demonstrate the effectiveness of the established results.