Finite-Time Stability Analysis And Controller Design Of Positive Switched Systems

Positive switching system consists of a number of positive subsystems,which are switched back and forth by some positive switching subsystems.It is not difficult to find from the published literature that most of the conclusions are about Lyapunov stability,which describes the system's ability to maintain steady state for a long time,but it can not achieve good performance in a short time.However,in the real operating system,if a system can not achieve the desired performance in a short period of time,even if the system is stable,it can not meet people's expectations.Therefore,it is of great significance to analyze the behavior change of the positive switching system in a short period of time,named the finite time stability.Based on the positive switching system research theory,this paper analyzes the problems of the finite time stability of the positive switching system and the synthesis of controller in a deeper level.This paper is divided into five chapters.The main analysis and research contents are as follows:For the positive-switched nonlinear system with time-varying delay,the cost function of the system is first given.Based on the method of mean dwell time(ADT),a finite time controller based on output feedback is designed.By constructing Lyapunov-Krasovskii function,sufficient conditions are obtained to make the closedloop system guaranteed finite time boundedness.Finally,a numerical example and a practical example are given,and the simulation module is built by Simulink in Matlab toolbox.The results show the effectiveness of the proposed method.For the discrete positive impulsive switched system,the cost function of the system is defined for the first time under the condition that the state is known.By constructing the multi-linear co-positive Lyapunov function,the problem of guaranteed cost finite time control of the system is analyzed by using the ADT method.Secondly,when the state is unknown,the positive observer and the non-fragile positive observer are designed to estimate the state of the system,respectively.Under the condition of ensuring the positivity of the error system,the state feedback controllers are designed respectively to make the closed-loop system finite time stability.For the continuous positive impulsive switched system,considering two kinds of external disturbances,asynchronous controller based on state feedback is designed,respectively.ADT method is adopted to obtain sufficient conditions for the input andoutput time stability of each subsystem under the action of the asynchronous controller.Secondly,for discrete positive impulsive switched system,two switching methods,ADT and model dependent mean dwell time(MDADT)are used to design an asynchronous controller,and the input-output finite time stability for the closed-loop system is considered.Finally,an example is presented to stress the availability of the proposed method.