基于改进型离散Wirtinger型不等式的时变时滞系统稳定性分析  

Stability analysis of time-varying delayed systems based on improved discrete wirtinger-based inequality

作　　者：田海生 龚德仁[1] 王楠 段登平[1] TIAN Hai-sheng;GONG De-ren;WANG Nan;DUAN Deng-ping(School of Aeronautics and Astronautics,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学航空航天学院

出　　处：《微电子学与计算机》2019年第10期21-26,共6页Microelectronics & Computer

基　　金：国家自然科学基金(61603249)

摘　　要：针对离散时变时滞系统的稳定性问题,采用改进型离散Wirtinger不等式方法进行研究,获得了一个保守性更低的稳定性判据.首先构造了一个新的辅助向量函数,利用正定矩阵的二次型都是正值的特性,提出了改进型Wirtinger不等式,获得了比传统的方法如离散Jensen不等式、离散Wirtinger不等式更好的求和逼近结果.在此基础上,构建了合适的Lyapunov-Krasovskii泛函,应用改进型离散Wirtinger不等式从而获得有更低保守性的稳定性判据,最终利用两个数值仿真完成验证.验证结果表明,利用新方法得到的时滞上界要大于现有的不等式方法,更接近理论值,从而表明了本文方法的有效性和优越性.In view of the stability analysis of linear discrete systems,an intense research has been conducted by adopting an improved discrete Wirtinger-based inequality.A new stability criterion of linear discrete systems with interval time-varying delay is derived,which yields less conservative stability conditions.By definition of a novel auxiliary function,we propose a better integral inequality and receive a tighter stability condition as compared to the recently results such as discrete Jensen inequality,discrete Wirtinger-based inequality.Based on the new inequality, we construct a dedicated Lyapunov-Krasovskii functional and obtain a tighter estimation of the derivative of Lyapunov-Krasovskii functional in terms of the new inequality.Finally,two numerical examples are given to demonstrate the efficiency of our new methods.

关 键 词：线性离散时滞系统 改进型离散Wirtinger不等式 稳定性分析 Lyapunov-Krasovskii泛函法 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]