基于新二重积分不等式中立时滞系统稳定性分析

Stability Analysis for Neutral Systems with Time Delays Via New Double Integral Inequality

针对线性中立时滞系统的时滞相关稳定性问题,本文对文献[7]中二重积分不等式进一步推广,提出了一个改进的二重积分不等式,通过利用改进的二重积分不等式和构造增广型的Lyapunov-Krasovskii泛函,由线性矩阵不等式给出了新的时滞相关稳定性判别准则,并应用数值例子进行验证。验证结果表明,本文与自由权矩阵方法和时滞分割方法相比,能够获得更大的时滞上限,说明所得结果的有效性和优越性。该研究对时变时滞系统的稳定性分析方法具有重要意义。

This paper is concerned with the problem of the delay-dependent stability analysis for neutral systems with time delay.An improved double integral inequality is derived,which is an extension of the double integral inequality in[7].Employing the proposed double integral inequality and constructing appropriate Lyapunov-Krasovskii functionals,a new delay-dependent stability criterion is obtained in terms of linear matrix inequalities.Numerical examples are given to obtain maximum admissible upper bounds which are larger than those using delay-decomposition methods and freematrix methods.The above illustrates the effectiveness and strength of the method.Thus,this theoretical research has certain significance to study the further improvement on analysis fortime-delay systems.