Stability Analysis And Stabilization Design For Several Classes Of Positive Switched Systems

Generally,hybrid systems include discrete-time dynamical systems,continuous-time dynamical systems,or both.The switched systems is a typical hybrid systems,which consists of a set of continuous or discrete subsystems and a set of switching rules that coordinate them.But in actual production and life,there is a kind of system whose state variables are all non-negative.These systems which are composed of non-negative state variables are called positive systems.Positive switched system combines the non-negative characteristic of positive system with the hybrid dynamic characteristic of switched systems,so it is very challenging to study the positive switched system.In this paper,stability analysis and stabilization design are carried out for several kinds of positive switched systems,the main work is as follows:The stability of continuous and discrete positive switched time-varying systems with time delays are studied.Based on the principle that the reverse-timer starts timing at the end of subsystem running time,a class of reverse-timer-dependent linear co-positive LyapunovKrasovskii functional is constructed.By using the newly constructed linear co-positive Lyapunov-Krasovskii functional and the average dwell time method,a sufficient condition for exponential stability of the system under the condition of average dwell time is given.Then,based on the stability criterion,the sufficient conditions for the existence of state estimation for positive switched time-delay systems are derived.The stability of discrete-time positive switched time-delay systems based on average dwell time is studied.By using the newly constructed Lyapunov-Krasovskii functional and the statevariable transformation technique,a sufficient condition for the exponential stability of discrete positive switched time-delay systems is obtained.The obtained stability conditions provide an effective scheme for studying the stability of discrete-time positive switched systems with timedelay,that is,to find the exponentially stable switching signals of positive switched systems with time-delay.Finally,the stability criteria of impulsive discrete-time positive switched systems are given.Exponential stabilization of positive switched system with time-varying delay and actuator saturation average dwell time switching is studied.By using multiple co-positive LyapunovKrasovskii functional method,the state feedback controllers of subsystems are designed,and a time-dependent switching rule is designed to adjust the ratio of the running time of the stable subsystems and the unstable subsystems,the sufficient conditions for stabilization of positive switched systems with unstable subsystems are given.In addition,convex hull technology is used to solve the problem of actuator saturation.