Stability And Dissipative Analysis Of Markov Jump System Based On Asynchronous Control

In actual engineering problems,random factors such as sudden changes in system operation,sudden changes in internal subsystem connections,and damage to system components often affect the entire system structure.Therefore,the Markov jump model is introduced to describe the characteristics of this type of system structure and provide a theoretical basis of solving engineering problems.In addition,in most existing work,it is usually assumed that the controller can obtain all system modal information,so that the controller modal can run synchronously with the system modal.Unfortunately,in practical applications,these ideal assumptions are difficult to meet due to unexpected factors such as time lag in the network control system,packet loss,and quantization.In order to overcome this strict limitation,asynchronous control method as one of the mainstream research methods has become an important research object of scholars.Therefore,in recent years,the use of asynchronous methods to study the control problems of Markov jump systems has attracted more and more attention.In this paper,the Markov jump system is controlled asynchronously by using Lyapunov's stability theory and linear matrix inequality technology.In the theorem proving process,Shure's complement lemma and sector boundary conditions are used.At the same time,when selecting the specific Markov jump system,this paper mainly introduces the unified model of the chaotic system and the time-delay recurrent neural network system.In this thesis,the Markov jump system is a hot topic in the field of control,and the research is carried out in the direction of asynchronous control.The following is the research content of this paper:First,a class of Markov jump systems with continuous time-delay characteristics is selected as the main research object.On the basis of this system,the control method of asynchronous control is introduced.The asynchronous phenomenon appears between the system mode and the controller mode,which is described by the hidden Markov model.By using the linear matrix inequality technique,sufficient conditions are obtained to ensure that the Markov jump system is stochastically stable and strictly dissipative.On this basis,a design method of asynchronous controllers is proposed,which can also be applied to independent mode controllers and synchronous controllers under special circumstances.Second,on the basis of the Markov jump model,the T-S fuzzy method is added,and the random stability and strict dissipative judgment criteria are used to design the asynchronous controller.First of all,considering the complexity of the system mode with a set of fuzzy rules,a suitable Lyapunov function is constructed to generate a dual-mode process according to the skip mode of the Markov jump system and the mode of the asynchronous controller.Then,by introducing a hidden Markov model,asynchronous phenomena can be shown between the controller and the Markov jump system.Secondly,through the linear matrix inequality technique,sufficient conditions can be obtained to ensure the random stability and strict dissipation of the Markov jump system.Finally,an example is used to verify the results.Third,on the basis of the second research result,sliding mode control is added to form a dissipative asynchronous fuzzy integral sliding mode control.Since the mode of the original system cannot be obtained directly,the hidden Markov model is used to detect the mode information.In addition,a suitable asynchronous integral sliding mode surface is designed to construct a suitable Lyapunov function.Through Lyapunov stability theory and linear matrix inequality technology,sufficient conditions are provided for the design of asynchronous sliding mode controllers.At the same time,this also ensures the random stability and good dissipation performance of the time-delay recursive Markov jump system.Finally,a numerical example is used to verify the effectiveness of the proposed method.Fourth,in order to enhance the feasibility of practical applications,considering that the methods used before and after the Markov jump system under study are different.In further research work,the theoretical results of the relevant chapters will be used in the actual system.This paper mainly considers the two actual systems of mass-spring-damper system and DC motor system.The mass-spring-damper system is an extremely important system in the mechanical system.The DC motor system is the most common motor system.The application of asynchronous control in the above-mentioned actual system can prove the practicability of the derived control method.