基于Wirtinger型积分不等式的线性时滞广义系统稳定性分析

Stability Analysis for Singular Systems with Time Delays Based on Wirtinger-Based Integral Inequality

针对线性时滞广义系统的稳定性问题,本研究通过适当的Lyapunov-Krasovskii泛函和Wirtinger型积分不等式方法,给出了新的时滞相关稳定的充分条件,并通过Matlab的LMI工具箱求解。数值算例表明,本文方法所获得的结果与自由权矩阵和时滞分割等方法相比,具有更小的保守性,说明本研究所获得的结果具有有效性和优越性。因此,该方法可以推广到区间时变时滞广义系统的稳定性研究和控制器设计中。

In this paper,delay-dependent stability analysis for linear singular systems with time delay is studied.By constructing an appropriate type of augmented Lyapunov-Krasovskii functional containing a triple integral term and using the Wirtinger-based inequality,a new delay-dependent stability criterion is established in terms of linear matrix inequalities,which could be solved by using LMI tools of Matlab.The present method could produce better results than those using delay-decomposition methods.A numerical example is given to illustrate the improvement of the upper bounds of time delay and the effectiveness of the present results.It can be expected that the present method is useful for dealing with singular systems with time-varying delays.