Finite Time Control Of Markov Jump Systems Based On Dynamic Event Triggered Mechanisms

Markovian jump system is a kind of random system with multi-systems.Markovian jump system represents the jump transition principle between different modes through a set of Markovian chains,so it can accurately model control systems which may have random sudden changes such as working environment changed,system damaged,system time-delay and so on.So far,most of the research results are based on Lyapunov stability,which concerns the steady-state performance of the system in infinite time.However,Lyapunov stability cannot represent the dynamic performance of the system.For example,it cannot represent the transient performance of the system.Therefore,some scholars began to discuss the finite-time stability,which focuses on the dynamic behavior of the system in the finite time interval and analyzes the astringency of the system in the finite-time interval.Finite-time stability not only provides quantitative information,but also improves the performance of the system.On the other hand,the dynamic event-triggered mechanism can effectively reduce the data transmission frequency between the control system modules,and ensure the good performance of the system while alleviating the network burden and saving resources.Therefore,it is of great significance to study the finite-time control of Markovian jump systems based on dynamic event triggering.This thesis considers the asynchronous control of Markovian jump systems based on dynamic event-triggered mechanism with finite-time stability.The main contents can be summarized as follows:1.Based on the dynamic event-triggered mechanism,the asynchronous control problem of discrete-time Markovian jump systems is studied.Based on the input-output finite-time stability,we obtained a sufficient condition for system convergence.At the same time,in order to alleviate the problems of communication congestion and data packet loss,we introduce the Round-Robin protocol.By using the linear matrix inequality method,the design method of controller gain matrix is obtained.2.For discrete-time Markovian jump systems with multiplicative noise,using Gronwall inequality,linear matrix inequality,Schur complement,Round-Robin protocol and other methods,the sufficient conditions for realizing the input-output finite-time stabilization of discrete-time Markovian jump systems with multiplicative noise are given.3.The finite time of continuous-time semi-Markovian jump systems triggered by events is studiedL₂-L_∞asynchronous control problem.we use linear matrix inequality and finite timeL₂-L_∞stability principles to design a state feedback controller.By constructing appropriate Lyapunov functions,we can get the sufficient conditions which based on system stability and controller gain matrix.