The Exponential Estimation Of The Solution Of Switched Positive Linear Systems

A switched system is a hybrid system consisting of a series of continuous or discrete subsystems and the rules that coordinate the switching between these subsystems.In recent years,we have witnessed the rapid development of the theory of switched systems.In real life,the values of the state variables of many actual dynamic systems are nonnegative or positive.Such systems are generally called to be positive systems in the literature.Due to the wide application of handover switched positive systems in biology,probability,communication and economy,more and more scholars begin to explore the theory of positive switched systems,especially the stability of positive switched linear systems.In the first chapter,we briefly introduce the development history,stability and exponential stability of switched systems and positive switching systems,and introduce the main contents of this paper.In the second chapter,the basic knowledge and the definitions of symbol are briefly introduced.In the third chapter,the exponential estimation of the solution of a positive switched linear system under arbitrary switching signal is studied.Firstly,the exponential estimation problem of continuous time positive switched linear systems under arbitrary switching signal is studied,and the calculation method of exponential decay rate for continuous time positive switched linear systems is given.Secondly,the exponential estimation problem of discrete time positive switched linear systems under arbitrary switching signal is studied,and the calculation method of exponential decay rate for discrete time positive switched linear systems is given.Finally,numerical examples and simulation results show the effectiveness of the results.