Research On Stability Of A Class Of Neutral Markovian Jumping System

The neutral Markov jumping system is a special class of switching system.The switching regular of the system can be described by Markovian process;Stability is one of the important properties of the system and has caused widespread research.In this paper,the stability of a class of neutral Markov jumping systems is researched and obtain relatively perfect,systematic and important results.The main research contents of this paper include the stochastic stability of neutral Markov jumping systems with time-varying delays,the exponential stability of nonlinear neutral Markov jump systems with time-varying delays,and the asymptotic stability of neutral Markov jumping systems with time-varying delays and distributed delays.1.The stochastic stability of a class of neutral Markov jumping system with time-varying delays is researched.Firstly,the Lyapunov function is constructed,and Jensen’s inequality and some matrix inequality analysis techniques are used to obtain sufficient conditions for satisfying stochastic stability.Secondly,these stability conditions can be solved by using the LMI toolbox in matlab.Finally,the numerical examples are given to verify the validity of the results obtained.2.The exponential stability of a class of neutral Markov jumping system with time-varying delays is researched.First,the criterion for satisfying the exponential stability is obtained by constructing the Lyapunov function and adopting the linear matrix inequality analysis technique.Follow these stability criteria can be solved using the LMI toolbox in matlab.At last,the validity of the results obtained is verified by numerical examples.3.The asymptotic stability of a class of neutral Markov jumping system with time-varying delays and distributed delays is researched.First of all,based on the definition of Asymptotic stability,the assumption of asymptotic stability criterion is obtained by using the linear matrix inequality.Next the LMI toolbox in matlab is used to solve these stability assumptions.Finally,the numerical examples are given to verify the validity of the results obtained.