Dissipativity Analysis For Lur’e Systems With Time Varying Delay

As a typical class of nonlinear systems,the nonlinear terms of Lur’e systems are usually defined in a finite sector interval or an infinite open plane.Many famous models can be summed up as Lur’e system.Little research results for Lur’e systems with additive time-varying delays(ATDs)and stochastic Lur’e systems with time-varying delay can be found.In this thesis,for those type of systems,the main works are summarized as follows.(1)The problem of dissipativity analysis is discussed for Lur’e systems with ATDs in this work.Based on the dynamic delay interval(DDI)method,some novel Lyapunov-Krasovskii functionals(LKFs)are constructed,in which part of Lyapunov matrices are requested to be positive definite.Then strictly dissipativity criteria of Lur’e systems with ATDs are presented in terms of linear matrix inequalities(LMIs).As by-products,the stability criteria of Lur’e systems with ATDs,Lur’e systems with time varying delay and the systems with ATDs are derived.Finally,several numerical examples are used to illustrate the effectiveness and superiority of these criteria.(2)The problem of dissipativity analysis is studied for a class of stochastic Lur’e systems with time-varying delay in this work.Based on the DDI method,the suitable LKFs are constructed by considering the characteristics of this type of systems.The weak infinitesimal generator can be obtained byI(?)formula and estimated by matrix inequality,and the extra variable will be introduced by constructing some zero equations,which hopes to reduce the conservatism of the criteria.By Schur complement,the strictly dissipativity criteria for stochastic time-varying delay Lur’e systems are obtained in terms of LMIs,similarly,the stability criteria are given as corollary.Finally,numerical example is given to illustrate the effectiveness of the obtained criteria.