Research On Nonlinear Semi-markov Jump Systems And Its Application On Multi-agents

Due to the complexity of environmental conditions and the demand of control accuracy,the models of controlled systems are becoming more and more complicated.Unexpected situation such as component failure,communication interruption and environmental change may cause stochastic changes of system structure.It leads to the fact that it is difficult to describe these systems by deterministic systems.In this case,Markov jump systems is suitable.However,the transition rate of Markov jump systems is time invariant,which limits the scope of application.Therefore,semiMarkov jump systems whose transition rate is time variant are proposed.It is of great theoretical significance and practical value to study semi-Markov jump systems.The systems mentioned above are centralized systems,with the development of industry,complex production tasks may not be completed only by a centralized system.Therefore,distributed systems are paid more attention,and multi-agent system is a typical type of distributed system.In practice,the communication topology of multi-agent systems may vary randomly due to environmental disturbance.Multi-agent systems with semi-Markov switching topology have attracted more and more researchers’ attention.This paper focuses on the stability analysis and synthesis of nonlinear semiMarkov jump systems and consensus of multi-agent systems with semi-Markov switching topology.The main work of this paper is shown in the following:The analysis and synthesis of nonlinear semi-Markov jump systems are studied.The nonlinearity is described by incremental quadratic constraint,which makes the controlled systems more general.Firstly,sufficient conditions of stochastic stability in the form of linear matrix inequalities are obtained by means of Lyapunov stability principle,S-procedure and slack variable method.Then,the existence conditions of controller,observer are achieved by the upper and down bounds method and slack variable method.Compared with the previous work,the sufficient conditions in this paper are less conservative and small computational.The stability analysis and stabilization of stochastic differential semi-Markov jump systems are investigated.Firstly,the mode-dependent It? formula of stochastic differential is presented.Sufficient conditions of stochastic stability in the form of linear matrix inequalities are achieved by means of Lyapunov stability principle,Sprocedure and slack variable method.Then,to give the sufficient conditions of controller gain matrix,slack variable method is used.Compared with previous results,the sufficient conditions are less conservative and less computationally intensive.Finally,the designed controller can eliminate the adverse effects of stochastic jumps,nonlinearity and random disturbances,which makes the controller more robust.The consensus problem of multi-agent systems with semi-Markov switching topology is studied.Firstly,the stability analysis of nonlinear semi-Markov jump systems with time-varying delays is considered,the sufficient conditions are in the form of linear matrix inequality.Then,the results are promoted to distributed systems,the consensus protocol designed for the multi-agent systems is based on the switching topology and comprehensive information.The protocol can ensure the consensus of systems even if the states of neighbor and expect are not fully available,which indicates the protocol is more robust.