具有时变时滞的中立型系统的指数稳定性  

Exponential Stability for Neutral Systems with Time-Varying Delays

作　　者：刘畅[1] 徐兆棣[1] 高杰[1] 

机构地区：[1]沈阳师范大学数学与系统科学学院,辽宁沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2010年第1期4-7,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省自然科学基金资助项目(2001101026)

摘　　要：研究具有时变时滞的中立型系统的指数稳定性问题。根据李雅普诺夫第二方法,构造适合讨论文中给定系统指数稳定性的李雅普诺夫函数,对积分交叉项的处理是通过引入一个使得结果保守性较小的不等式,并在此基础上得到了一个关于中立型系统时滞相关的指数稳定性判据。同时,根据针对中立系统所提出的方法又总结出了使得时滞微分动力系统时滞相关的指数稳定性判据,得到了求解时滞相关最大上界的算法,最后利用MATLAB中线性矩阵不等式LMI工具箱求解,得到使得文中所讨论系统指数稳定的时滞最大上界和指数稳定的最大上界。最后通过数值例子说明结果的可行性、正确性和有效性。In this paper, we consider exponential stability for neutral systems with mixed time-varying delays. Based on the Lyapunov second method, construct a suitable Lyapunov function for exponential stability of the given system in the discussion. In order to deal with the item of integral cross-term, and by using an integral inequality to obtain a less conservative conclusion, a delay-dependent criterion for exponential stability of the neutral system is derived. In the mean while, according to the neutral system proposed, we obtain a delay-dependent criterion for exponential stability of the differential dynamical systems with time delays, while the largest upper bound algorithmin for the time delays is given. At last empolying linear matrix inequality （LMI） toolbox in this work, it provides larger time-delay bounds and convergence rates. Numerical examples are illustrated to show the feasibility, accuracy and effectiveness of our results.

关 键 词：中立系统 时滞 指数稳定 李雅普诺夫方法 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]