Finite-time Stability Of Linear Singular Differential Systems

Stability is an important research topic of differential equations,and its research results have been widely used in control theory,biological engineering,physics,power systems and other fields.Compared with global stability,stability in a finite time can be more well represent the transient behavior of the system in a certain time interval.Since the finite time stability was proposed by the Soviet scholar ?.?.Kamankov,it has been widely used in different projects,so the finite time stability has gradually become an important subject of differential equations.At the same time,in the actual system,there are many factors affecting system performance,including singular and time delay factors.Singular differential systems have been widely used in economic models,aerospace engineering,biological systems and other fields,and people have paid great attention to it.Differential system with time delay often appear in many fields such as economics and control theory.Therefore,the stability analysis of time delay and singular differential systems has also been a research hot spot.This paper mainly studies the effects of time delay and singular factors on the finite time stability of the system.The fractional order differential system is extended from integer order to fractional order.The linear matrix inequality and Lyapunov function are used to discuss the finite time stability of integer order linear singular impulsive differential systems with delay,the finite time stabilization of fractional order linear singular differential systems,and the finite time stability of fractional order singular differential systems with delay.The work mainly includes the following chapters:In the first chapter,the development and research significance of finite time stability and the differential system involved in this article are introduced briefly.In the second chapter,the finite time stability problem of integer order linear singular impulsive differential systems with delay is studied.By constructing the Lyapunov function,sufficient conditions are obtained to make the linear singular impulsive differential systems with delay stable in finite time.On this basis,the system is further studied in the absence of disturbance,sufficient conditions that can make it stable for a limited time.Finally,the correctness of the research results is illustrated by actual examples.In the third chapter,we study the finite time stabilization problem of fractional order linear singular differential systems.For the problem of fractional order singular differential systems,by constructing the Lyapunov function method,we design the state feedback controller of the system,and obtain that the system can be tolerated in finite time.The conditions of internal stabilization.Finally,the simulation results illustrate the correctness of the research results.In the fourth chapter,based on chapter 3,the fractional order linear singular differential system is extended to fractional order singular differential systems with delay.By constructing the Lyapunov function and using the inequality technique of linear matrices,the fractional singular differential system with delay is stable in a finite time.Sufficient conditions for simulation.Finally,the simulation results show the correctness of the research results.