Dynamic Analysis And Control Of Non-homogeneous Markov Jump Hybrid System

In practical life,random phenomena are widespread.Among them,using the random switching signal of Markov process to describe the switching between modes in the hybrid system has attracted wide attention from scholars.The dynamic characteristics of a hybrid system with a Markov process can be described by both discrete events and continuous variables.In terms of actual system modeling,this system has greater advantages than non-jumping systems.At present,in most of the related literatures containing Markov jump discrete hybrid systems,scholars assume that this type of Markov chain is homogeneous,that is,the transition probability matrix is fixed.However,in the actual system,due to the influence of environment and other factors,the transition probability matrix is related to time.In order to describe the model of the complex system more accurately,it is of great significance to study the non-homogeneous Markov jump hybrid system.This paper mainly discusses the stability of nonlinear systems with non-homogeneous Markov jumps,controller design,and finite field stability.The main research contents are summarized as follows:1.The finite-time stability of a class of discrete-time non-homogeneous Markov jump nonlinear systems is studied.In the context of the T-S fuzzy system,the T-S fuzzy system with non-homogeneous Markov jumps is first established,and the fuzzy error dynamic system with uncertain norm bounded parameters is further considered.Then,with appropriate stochastic Lyapunov functions,and using related theoretical knowledge such as Shure's complement lemma and stochastic analysis,the sufficient conditions for the random finite time bounded fuzzy error dynamic system are obtained.Finally,a specific filter is used to verify the effectiveness and correctness of the method.2.On the basis of Markov jump system,the problem of finite-time bounding and H? filtering of a class of discrete-time semi-Markov jump fuzzy systems is studied.First,through the theories of finite-time stability and ? error mean square stable,redefine the concepts of finite-time stability and finite-time bounded semi-Markov jump hybrid systems.Secondly,using methods such as stochastic analysis and linear matrix inequality,the fuzzy error dynamic system is given a ? stochastic finite time bounded and sufficient conditions for H? performance.Finally,a type of H? fuzzy filter is designed.The feasible parameters of this type of fuzzy filter can be solved by the Matlab toolbox.Numerical simulations verify the effectiveness of the method.3.The input and output finite area stability and controller problems of the T-S fuzzy two-dimensional discrete Roesser model with non-homogeneous Markov jumps are discussed.First,the discrete Roesser model is used to establish a two-dimensional non-homogeneous Markov jump T-S fuzzy system.Secondly,considering the influence of external disturbance on the T-S fuzzy two-dimensional discrete Roesser system,the concept of finite field stability of the system is given.Then,according to the type of external interference,different input and output finite field stability standards were formulated.These standards are given in the form of linear matrix inequalities.Finally,an asynchronous state feedback controller is designed to make the system stable in a limited area under disturbance conditions.Numerical simulations verify the effectiveness of the proposed technology.