基于二阶近似积分不等式的时滞系统稳定性分析  

Stability Analysis of Time Delays Systems Based Second-order Approximation Integral Inequality

作　　者：王楠 龚德仁[1] 许光坦 段登平[1] WANG Nan;GONG De-ren;XU Guang-tan;DUAN Deng-ping(The School of Aeronautics and Astronautics, Shanghai Jiaotong University, Shanghai 200240, China)

机构地区：[1]上海交通大学航空航天学院,上海200240

出　　处：《科学技术与工程》2020年第22期9097-9101,共5页Science Technology and Engineering

基　　金：国家重点实验室开放基金(19Z1240010018)。

摘　　要：提出了一种新的积分不等式,称为二阶近似积分不等式(second-order approach integral inequality,SAII)。著名的积分不等式如Jensen不等式和基于Wirtinger的不等式均是本文所提的二阶近似积分不等式的特例,并且进一步证明了Jensen不等式和Wirtinger不等式分别是所提不等式的零阶和一阶近似。在所提二阶近似积分不等式基础上,提出了一种适用于时滞系统的稳定性判据。最后,算例表明了该方法的有效性和优越性。A new integral inequality,also known as second-order approximation integral inequality(SAII),was proposed,which could significantly reduce the conservativeness in stability analysis of systems with time delays.The former well-known integral inequalities such as Jensen’s inequality and Wirtinger based inequality,were special cases of the proposed SAII.Furthermore,it could be inferred that Jensen’s and Wirtinger based inequalities were just zero-order and first-order approximation,respectively.A stability criterion with less conservatism was then developed on SAII for time delay systems.Numerical examples demonstrated the effectiveness and benefit of the proposed method.

关 键 词：线性参数系统 线性系统的稳定性 时滞系统 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]