The Research Of Finite-Time Stability For A Class Of Time-Varying Stochastic Systems

Time-varying systems exist widely in nature and engineering fields.For example,systems in complex system process control,robot motion control,aerospace and other fields are more or less time-varying.A timevarying system means that the parameters of the system change with time.When one or more parameters in the system change with time,the characteristics of the entire system will also change with the passage of time.In recent years,the research of time-varying systems has attracted the attention of many experts and scholars,and relevant theoretical methods continue to emerge and mature.However,there are still many substantial difficulties in the research of stability of time-varying systems that need to be further explored.Many challenging fields such as communications and information technology involve system time interval.The time interval causes the current state of the system to be affected to a certain extent by the historical state of the system,which may lead to instability and fluctuation of the system.On the other hand,the system will inevitably be affected by stochastic noise in practical applications.Studying the properties of stochastic differential equations can better study the characteristics of time-varying systems in noisy environments.Finite-time stability refers to the study of the stability of the system within a limited time interval,under the premise of given initial conditions,the state of the system does not exceed a certain threshold for a certain period of time,then the system is said to be in a certain period of time.The time interval is stable for a finite-time.This is a concept with a wide application background,requiring the dynamic system state trajectory to be kept within the ideal operating range within a certain time interval to prevent saturation,meet hardware constraints,or maintain the linearity of the system.This paper will study the stochastic finite-time stability of linear stochastic systems and linear stochastic time-delay systems respectively.For time-invariant systems,especially linear time-invariant systems and their related stability theoretical research,a series of abundant research results have been obtained.However,for linear time-varying systems,it is worth pointing out that the related theoretical results of the stability of linear time-invariant systems cannot be directly applied to the study of time-varying systems in most cases,such as the time-varying systems of linear time-varying systems.The variable system matrix is difficult to analyze the properties of its eigenvalues,and the linear matrix inequality method in the stability study of linear time-varying systems is also difficult to apply to linear time-varying systems.Therefore,this article uses the piecewise analysis method and stochastic analysis techniques to first analyze the changes in the system state of the linear time-varying stochastic system in the piecewise interval,and then use the piecewise approximation method,using stochastic differential equations and Ito’s lemma to prove The stochastic finite-time stability of the system,and the idea of designing the controller in sections according to the linear matrix inequality method,enables the designed controller to be effectively realized.According to the research results,the state feedback controller of the system is designed.Finally,several examples are used to verify the effectiveness of this method.The main content of this paper is summarized:Chapter 1 describes the research background and significance of the finite-time stability of timevarying stochastic systems and time-varying stochastic time-delay systems,and introduces the stochastic finite-time stability of time-varying stochastic systems and time-varying stochastic time-delay systems.Finally,the framework and main content of this article are sorted out;Chapter 2 studies the stochastic finite-time stability and controller design of linear timevarying stochastic systems.First,assuming that a specific Lyapunov function satisfies piecewise continuity,anew method of finite time stability that may be discontinuous at each piecewise point is proposed.Finally,a class of linear time-varying stochastic systems is designed based on linear matrix inequalities.The algorithm of stochastic finite-time stable controller;Chapter 3 refers to the research idea of finite-time stability of time-varying stochastic system under the rules of stochastic time-delay system.The new method of continuous finite time stability,and the finite time stability of time-varying stochastic time-delay systems with the help of switching systems;Chapter 4 summarizes and sorts out the research results of this paper.At the same time,in view of the deficiencies in the research of this article,the direction of future research is proposed.