Finite-time Stabilization Of Switched Positive Systems

The switching positive system consists of a limited number of positive subsystems and a set of signals that control the switching of the subsystems.Switched positive systems have both the complex dynamic behavior characteristics of the switched systems and the unique state non-negative characteristics of the positive systems.Therefore,the research on the related problems of this type of systems are relatively difficult.The switched positive systems are widely used in the field of control,and is closely related to many life fields such as economy,biology,communication,etc.,which have attracted great attention from scholars.In practical applications,the short-term dynamic change of the system behavior is very important.Many systems meet the stability performance of an infinite time interval but cannot meet the performance indicators in a short time interval.Typical infinite time interval stability,such as Lyapunov asymptotic stability,is relatively independent of the concept of finite time stability.The Lyapunov asymptotic stability of a system does not necessarily satisfy finite time stability,and vice versa.Therefore,the research on the finite-time control of the switched positive systems has a certain theoretical depth and practical application value.Based on the average dwell time method,this paper adopts the copositive Lyapunov function method to further study the finite-time stability of the switched positive systems.The main research content of this article is divided into the following parts:(1)Based on the average dwell time switching law,a kind of slow switching law,the copositive Lyapunov function is taken instead of the quadratic Lyapunov function method to analyze the finite-time stability of the linear switched positive system;The switching law we designed meets the average dwell time and makes the system meet the given transient performance index.Compared with the traditional quadratic Lyapunov function,the non-quadratic copositive Lyapunov function method not only has a concise mathematical description,but also can reflect the non-negative characteristics of the system.(2)For a class of asynchronous switching positive systems with time delays,firstly,dividing the operating interval of each positive subsystem into the matching and mismatching intervals between the subsystem and the controller,and then combine the average dwell time switching theory and the multiple copositive Lyapunov-krasovskii functional method,the appropriate switching laws and the existence conditions of the state feedback controller are given in the form of linear matrix inequalities,so that the system is finite-time stable and the non-negative characteristics of the system are retained.(3)Researching the finite-time stabilization problem of the time-delay switched positive systems when the actuator is saturated.Using the convex combination method,the saturated nonlinear controller is transformed into a combination of a set of linear controllers.This research method has the advantages of low conservativeness and convenient controller solution.Finally,the sufficient conditions for the design of the switching law and state feedback controller gain matrix are obtained,and a detailed solution algorithm is given to ensure that the system is stable in a finite time and is still a switched positive system.