New Stability Criteria Research And Applications For Time-delay Systems Based On Improved Lyapunov Functional

Time delays are often encountered in various practical systems such as electricity,metallurgy, chemical process, aerospace, communication, transportaion, and so on. Muchattention have been paid to time-delay systems due to the fact that they have importantpractical applications. Meanwhile, time delays are the key factor in many control systemsbecause they often lead to poor performance, or even instability. Thus, the research onstability and control for time-delay systems is important both in theory and in practice.In this dissertation, the improved Lyapunov-Krasovskii functionals are studied usingthe delay-decomposition method and inequality technique. The stability issues oftime-delay systems are investigated with the help of LMI tools. The major contributions ofthis thesis are as follows:(1) The stability of linear neutral system with time-delay is studied. The Lyapunov-Krasovskii functionals are constructed by the delay-decomposition approach. The delayinterval is decomposed into some subintervals. The different weighting matrices arechosen for each subinterval. By using reciprocally convex combination inequality, theuseful information of time-varying delay is considered. The novel delay-dependentstability criteria are obtained in terms of LMIs through using slack matrices. The improveddelay bounds and less conservativeness of criteria over some reported results areillustrated by numerical examples.(2) The consensus of multi-agent systems consisted of linear systems is considered.There are communication delays between the multi-agents. The delayed state feedbackcontroller for the multi-agent systems is investigated. Both fixed topology and switchingtopologies are considered. Through system transformations, the consensus proble isconverted to the delay-dependent stability problem of error system. By constructingproper Lyapunov-Krasovskii functional, using Wirtinger inequality, the stability criteria ofmulti-agent systems, which are dependent on the sizes of delay, are derived in the terms ofLMIs. The relationship between parameter of controller and delay bound is given. Finally,two numerical examples are given to show the merits of our derived method. (3) The problem of stability is considered for nonlinear neural network system withtime-varying delay. The Lyapunov-Krasovskii functionals are constructed by thedelay-decomposition approach. The delay interval is decomposed into some subintervals.The different weighting matrices are chosen in each subinterval. More information of theslope of neural activation functions is utilized. By using reciprocally convex combinationinequality, the useful information of time-varying delays is considered. The derivedstability criteria are less conservative than some reported results. Finally, two numericalexamples are given to demonstrate the effectiveness of the proposed criteria.(4) The problem of master-slave synchronization of Lur’e systems is considered. Thedelayed state feedback controller is investigated. The problem of synchronization istransformed into stability of error system. The Lyapunov-Krasovskii functionals areconstructed by the delay-decomposition approach. The delay interval is decomposed intosome subintervals. The different weighting matrices are chosen in each subinterval. Moreinformation of the slope of Lur’e systems is utilized. By using reciprocally convexcombination inequality, the useful information of time-varying delays is considered. Thenovel delay-dependent stability criteria are obtained through using slack matrices. Therelationship between parameter of controller and delay bound are given. Lessconservativeness of criteria over some reported results is illustrated by numericalexamples.(5) The sampled-data control synchronization problem is conserned for two identicalchaotic Lur’e systems. The sampled-data control method is employed in the system. Thesampling period is time-varying. The problem of synchronization is transformed intostability of error system. The segmented differencial Lyapunov-Krasovskii functional isconsidered. The information of the sampling time is utilized. The positive definiteness ofthe functional is guaranteed using the slack matrices. The novel delay-dependent stabilitycriteria are obtained. The relationship between parameter of controller and maximumsampling period is given. The results show the effectiveness of the proposed criteria.(6) The issue of stability for the bilateral teleoperation system is concerned. There arecommunication delays between master and slave. The delays are time-varying andasymmetric. Two classes of controllers: delayed position-error feedback and delayed torque feedback are designed. The new Lyapunov-Krasovskii functional is constructed. Byusing reciprocally convex combination inequality, the useful information of time-varyingdelays is considered. The stability criteria are shown under specific LMIs. Finally, bothsimulations and experiments are performed to show the effectiveness of the proposedmethod.