The Research And Application Of Stability For A Class Of Time-varying Stochastic Systems

Time-varying systems widely exist in the field of engineering and nature.For example,time-varying systems exist in many fields such as aerospace,robot motion control,and complex system process control.A time-varying 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 time.At present,many experts and scholars in the world are dedicated to researching various properties of time-varying systems.As we all know,Sampled-data control theory and stability are two important properties of time-varying systems,and they are also popular topics around the world.Although the research on this kind of subject is becoming more and more in-depth today,there are still a lot of substantial difficulties that.need to be resolved in the research on the stability of time-varying systems.Similarly,there are various time lag problems in real life.The study of time-delay systems is extremely important.The purpose of reducing the conservativeness of the stability criterion is to analyze the stability of time-delay systems.The stability condition of a time-delay system means that the system parameters can satisfy the stability of system when the time-delay of the system does not reach the upper bound of a certain time-delay.Therefore,the main factor for judging the conservativeness of the delay condition is the maximum allowable delay.At the same time,in practical applications,systems are often inevitably affected by stochastic noise.The study of stochastic differential equations and related properties is helpful to study the relevant characteristics of time-varying systems in a noisy situation.This paper will study the stability of linear time-varying stochastic systems and time-delay systems respectively.For several reasons,the stability analysis of linear time-varying systems is much more complicated than linear time-invariant systems.And for time-invariant systems,especially linear time-invariant systems and their related stability theoretical research,a series of fruitful 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 can not be directly applied to the research of time-varying systems in most cases.Therefore,the research on the stability of time-varying systems in this article has certain scientific significance and theoretical value.This paper studies the stability of a class of linear time-varying systems.First,the stability of linear time-varying systems under stochastic systems is discussed.Secondly,the stability under the stochastic timedelay system is considered.The main content of this article is summarized as follows:In chapter 1,describes the research background and significance of time-varying stochastic systems and stochastic systems under the rules of time-varying stochastic time-delay systems;introduces the qualitative research status of time-varying stochastic systems and time-varying stochastic time-delay systems at home and abroad;Finally,the framework and main content of this article are sorted out.In chapter 2,for the sampled-data control of time-varying stochastic systems,it is necessary to use stochastic analysis methods for research,and the analysis methods are far more complex than deterministic systems.In this chapter,the stabilization of a class of time-varying stochastic systems is studied.In this chapter,based on the constant variation method and generalized Halanay's inequality,the criteria for the global uniform exponential stability and the global uniform asymptotic stability of linear time-varying stochastic systems are studied.In chapter 3,the sampled-data control of a time-varying stochastic system is transformed into a time-varying stochastic time-delay system,and the comparison principle of Halanay-type inequalities is proposed to ensure the stability of the stochastic time-delay system.Finally,through the proposed general Halanay-type inequality,the p-th moment stability,pth moment asymptotic stability and p-th moment exponential stability are studied,and a time-delay analysis method for sampled-data control of a class of time-varying stochastic systems is obtained.