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

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.