Quadratic Performance Analysis Of Switched Affine Systems

There are variety of systems in the real world,such as mechanical and electrical systems,manufacturing systems,power systems,communication systems,etc.,in the field of engineering,biological systems,ecosystems,and climate systems,etc.,in the field of natural as well as economic systems,population systems,social systems,and so on in the field of the society.Due the wide range of applications,systems have already received people’s concern.The analysis of stability for switched system is especially interesting,and has been one of heat issues since the 1990s.In the scientific researches and social productions,researchers often use a large number of systems with simple structure or simple function.These systems with simple structure or simple function are designed as switched systems by appropriate switching strategy to replace the expensive and single system to implement complexity tasks.Such switched systems can greatly improve the efficiency.At the same time,the applications of switched systems are based on the theoretical basis of systems.Thus,the researches for switched systems gradually become a frontier subject.In this paper,based on control theory,Lyapunov stability theory and matrix the-ory,the problems about quadratic performance of switched affine systems are studied including stability,tracking and L2 gain.Some relevant theoretical results have been obtained.Finally,the tool of MATLAB is used to verify the correctness of the theory.The main contents of the paper are described as follows.The first chapter introduce the background and the research status of switched systems,and gives some basic definitions and preliminaries of the paper.In second chapter,we study the problems about quadratic performance of switched affine systems including stability,tracking and L2 gain.A sufficient condition is given to solve the quadratic performance problem by using Lyapunov stability theory.Finally,the effectiveness of the control mechanism is demonstrated by numerical examples.In chapter three,we extend the time-invariant situation in second chapter to the time-varying situation,namely,both subsystem matrices and affine vectors are depend on time t.By using the method of Lyapunov stability theory and differential matrix inequality,sufficient conditions can be obtained to make the above quadratic behavior problem achieve.Finally,the effectiveness of the control mechanisms are demonstrated by numerical examples by using the tool of MATLAB.In chapter four,we summary our works and make a prospect for the future work.