State Feedback Control Of Discrete Time Switched Systems

A switched system is a hybrid system which is composed of a family of continuous-time or discrete-time subsystems and a rule which governs the switching between them. It can be used in the engineering system model to change the power structure and environmental factors. When studying switched systems, we are mostly focused on its stability, because the stability of the system is the foundation of system work better, and the stability of the system has extensive practical value, in the actual production, the equipment can be carried out only on the premise of stable state, due to the whole system not only depends on the stability of the subsystem, but also the selected switching strategy, adding to time delay and uncertainty, it’s more complicated to research the stability of the system, which has attracted more and more attention of scholars.This paper will study the stability of the switched base on state feedback method to systems. The system state feedback controller is designed according to the principle of stability and the definition of quadratic stability. we will study the stability of the closed-loop system by the state variable substitution, Schur complement lemma and LMI toolbox. This paper will study the switched system with time delay, uncertainties and time delays and uncertainties hybrid.The first chapter introduces the concept of hybrid system and switching system, emphatically illustrates the research value of switched systems, and analyses the switched systems with time-delay and uncertain phenomenon, finally, the paper introduced the research method and research content of this article. The second chapter studies the state feedback problem to the discrete switched systems with time-delay, first remove the time-delay system by the state variable substitution method, and study the stability of the closed-loop system through constructing a state feedback controller with the Schur complement lemma and the stability of switched system, and gives a sufficient condition of state feedback stabilization by the form of linear matrix inequality. The third chapter will study the cost control problem to the switched systems with time-delay and uncertainty, first of all, introduces the definition of quadratic stability of the system, system cost upper bound and guaranteed cost control, and gives four theorem of stability through constructing state feedback controller with switching system stability theory and the lemma which removes the uncertainty. The fourth chapter studies the fault-tolerant control problems to switched systems with the multiple time-delay and uncertainty, first, gives two lemma in dealing with the problem of zooming,next, designs the state feedback controller with memory to the problem of actuator failure and the delay in the state feedback and gives the corresponding theorems through the fault-tolerant control. At the end of each chapter, the numerical examples are given to demonstrate the effectiveness and applicability. Finally, we give the conclusion of the paper, and what to do in the future.