The Robust L₂-l_∞Problems Of Discrete Time Switched Systems

A switched system is a hybrid system that is composed of a family of continuous-time or discrete-time subsystems and a rule orchestrating the switching between thesubsystems. At any given time, a particular subsystem may be chosen by some’advanced process’, such as a controller, a calculator or manual operation, at this pointwe say the system is controlled. There may also be a function of time, or state, or bothof the time and state, which in this case we say that the system is autonomous. Inrecent years, the switched systems had been attaches great researchers who are incontrol field attention due to its own characteristics, especially about the autonomoussystems. The result has been applied to many valuable practical problems now.The problem ofl₂-l_∞filtering calculation rules was put forward by Wilson in1989, because it can deal with the problems of discrete time switched systems withuncertainties well, it also attracted widespread attention, and started applying in thepractical application of system engineering, such as control of the machine. Thecontent of this thesis is mainly about the switched system robustl₂-l_∞problems.Based on the first and second Lyapunov stability theory, by constructing Lyapunovfunctions, by using the operator, the piecewise Lyapunov function and linearmatrix inequalities methods, we study the considered system, in order to obtain thesufficient conditions that switched system is asymptotically stable and the supremumofl₂-l_∞performance indicators.In the first chapter, we mainly introduced the significance to research theswitched system and the research status ofl₂-l_∞filtering problem. The problem ofstability andl₂-l_∞performance of the discrete time switched systems withuncertainties problems were studied by using the operator in the second chapter.The stability and the guaranteed cost filtering problem of discrete time switchedsystem were studied by the linear matrix inequalities in the third chapter. In the fourth chapter we dealt with the stability of discrete time switched systems and the controllerproblem by using piecewise Lyapunov functions method. At the end of each chapter,there are numerical examples, which were used to verify the effectiveness andfeasibility of the results. Finally, we gave a summary of the whole article, and whatshould do in the future.