Exponentially Asymptotic Stability And Stabilization For A Class Of Uncertain Switched Distributed Parameter System With Time-delay

Switched system is an important class of hybrid dynamical systems. With thedevelopment of the research on the hybrid dynamical system, the meaning of the switchedsystem is becoming more and more practical. Switched system is composed by lots ofsub-systems and switching rules. Due to the existence of the switching signals, the research onthe switched system is much special and complicated than other researches on similar systems.Time delay exists in the practical controlling systems and the existence of it makes the systemunstable and generates inaccurate functions. At the same time, the system characteristics orthe perturbation of the parameter (the uncertainty of the system) is always inevitable.Therefore, the research on the stability and stabilization controlling of the uncertain time delayswitched system shows prominently theoretical value and practical meaning.This paper is concerned withL2(Ω)-exponentially asymptotic stability and stabilizationissues for switched distributed parameter system. By using a newly constructed MultipleLyapunov–Krasovskii functional technique and the minimal dwell time approach,delay-dependent sufficient conditions are derived for the considered system to beexponentially asymptotically stable. And then, the memoryless state-feedback controller isderived for the switched control system mainly computed from a new class of linear matrixinequalities (LMIs). All the conditions obtained in this paper are delayed dependent. Finally, anumerical simulation example is given to demonstrate the effectiveness of the proposedmethod.The structure of the essay is as following:The first chapter introduces the basic concepts and preparing knowledge of thedistributed parameter system, switched system, time delay switched system and etc. The second chapter focuses on the distributed parameter switched system with the delayof time-varying.The third chapter establishes the exponential asymptotic stable conditions of thedistributed parameter switched system with the time-varying delay.The forth chapter analyses the issues of exponential asymptotic stabilization of thedistributed parameter switched system with the delay of time-varying.The fifth chapter considers robust stabilization which is designed by the lack of memoryreaction controller of uncertain switched system.The sixth chapter proves the validity of the results by a simulation example.The seventh chapter summarizes the whole research and proposes some related issueswhich are worth studying.