Analysis Of Stability For MARKOV Jump System And Application In Consensus Control For Multi-agent System

With the development of Robotic technology and the widely use of communication network,in recent years,stochastic systems become more and more popular in many fields.Multi-agent system is one of the hot topics in current research directions.However,in network,communication limits,time delay and obstacles are always unavoidable during data transimission,which cause that the topology of communication switch randomly rather than remain invariant.Therefore,the theoretical research of stochastic systems and its application in multi-agent system have a very important role.This paper studies the problems of H_?control for a class of stochastic system and multi-agent systems with switching communication topologies.The main contents are as follows:Firstly,the H_? stability of a class of singular Markov jump system is studied.For the unmesurable of system states,the observer with output quantization is established.To obtain the H_?stability of the system,the sliding mode controller is designed based on the observer.Based on the observer and the controller,we construct the Lyapunov function and derive the sufficient condition of the H_?stability.The effectiveness of the proposed method is verified through simulation.Secondly,the consensus control of Leader-follower multi-agent system based on semi-Markov process is studied.For the time delay and actuator fault existed in the system,we transfer the mean-square consensus problem into the stability problem of the error system through the linear transformation.Then,we design the consensus control law and linearize the matrices of the error system.The problem of nonlinear terms generated by the unknown matrices of controller is solved and the H_?index is obtained by solving a group of linear matrices inequalities.The effectiveness of the designed control law is verified by simulation.Finally,the consensus control of multi-agent system based on semi-Markov process is studied.For the time delay and nonlinear terms existed in the system,we design the feedback control law.We transfer the consensus problem into the stability problem of the error system via the linear transformation.Then,we deal with the nonlinear problem of the transition rates of the semi-Markov process through the linearization.By sovling the linear matrix inequalities,we can obtain the controller gain matrices and get the H_? index of the system,at the same time,we derive the sufficient condition of system's consensus.The effectiveness of the designed control law is verified by simulation.