基于积分不等式法的区间变时滞不确定系统鲁棒稳定性研究

Integral Inequality Approach to the Robust Stability Criteria for Interval Time-varying Delay

研究了一类区间变时滞不确定系统鲁棒稳定性问题.在不确定性为泛数有界的情况下,通过构造包含简单积分项和多重积分项的Lyapunov-Krasovskii泛函,结合新的积分不等式,在未忽略有用项的前提下,利用其更紧的界定条件来处理交叉项,从而建立了基于线性矩阵不等式(LMI)形式的时滞相关稳定性新判据.方法不涉及自由权矩阵技术和任何模型变抱,减少了理论和计算上的复杂性.数值算例表明,所提出的判据是有效的,和一些已有文献相比具有更低的保守性.

This paper investigates the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay. Under the norm-bounded uncertain- ties condition, By constructing a new Lyapunov-Krasovskii functional which contains some simple integral terms and triple integral terms , combined with a new integral inequalities, the cross-term is tightly bounded without neglecting any useful terms in the stability analysis, A delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities （LMIs）. The proposed approach involves neither free-weighting matrix nor any model transformation, so that it can reduce the complexity both in theory and in computation. Finally, numerical examples are given to illustrate the effectiveness and an improvement over some existing results in the literature with the proposed results.