含非线性扰动的混合变时滞中立系统鲁棒稳定性新判据

New Robust Stability Criteria for Neutral Systems with Mixed Time-varying Delays and Nonlinear Perturbation

中立型时滞系统在工程实际中有着广泛应用背景.本文研究了一类含非线性扰动的混合变时滞中立型系统地鲁棒稳定性问题.基于直接Lyapunov泛函方法,通过构造一类新的包含时滞区间上下界的三重积分项Lyapunov-Krasovskii泛函,并结合积分不等式方法、自由权矩阵技术和凸组合处理方法,建立了一种新的线性矩阵不等式形式的离散时滞和中立时滞均相关的鲁棒稳定性判据.最后,通过数值算例验证了新判据的有效性和优越性,和一些已有文献相比,本文提出的判据具有更低的保守性.

Neutral time delay system is a special system which has wide application in prac-tical systems. In this paper, we consider the delay-dependent robust stability problem for neutral system with mixed time-varying delays and nonlinear perturbation. Based on the direct Lyapunov method, a new Lyapunov-Krasovskii （L-K） functional with triple integral terms involving lower and upper bounds of interval time-varying delays is constructed for the system. Then, combined with the integral inequalities method, the free weighting matrix approach and the convex combination technique, a neutral and discrete delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities （LMIs）. Finally, the numerical examples are presented to illustrate the effectiveness and improvement over some existing results in the literature with the proposed results.