Stability And Synchronization Analysis For Markovian Jump Delayed Lur’e Systems

As an important branch of stochastic switching systems,Markovian jump systems are often used to describe the systems in which the parameters and structures change abruptly.Markov jumping phenomenon is widely existed in complex networks,automatic control,robot arms and other practical systems.Besides,the nonlinear phenomenon is very common in practical control systems,and Lur’e system which is a typical nonlinear system has been applied in practical engineering extensively.Therefore,it is of great significance to do research on the Markov jumping Lur’e systems.This paper mainly studies the following two aspects of the markovian jump Lur’e systems: one is the stability analysis of markov jumping neutral delayed Lur’e systems,and the other is the synchronization analysis for markovian jump Lur’e systems with timevarying delay.The details are as follows:The previous Jensen-type integral inequality is improved in the first part.By using the incomplete-orthogonal polynomials method and the free-weighing-matrix technique,the Jensen-type inequality is improved in this paper and the less conservative free-matrixbased integral inequality is gained.The second part analyzes the stability issue of markov jumping neutral delayed Lur’e systems.The stability problem for neutral Lur’e system with time-delay is firstly considered in this paper.By studying the characteristics of the neutral delayed Lur’e system,combined with theories of Lyapunov functional,integral inequality and convex optimization,newly stability criteria are established.Then the method is applied to investigate the stochastic stability problem of markovian jump neutral Lur’e systems with time-delay,and the delay-dependent stochastic stability conditions are attained.Finally,some examples are offered to illustrate the correctness and effectiveness of the results.The stablization issue of markov jumping Lur’e systems with time-varying delay are analyzed in the third part.Firstly,based on the improved integral inequality,the synchronization issue of delayed Lur’e systems is explored by combing the new Lyapunov functional,the delayed partition and the reciprocally convex combination method,and the less conservative delay-dependent synchronization conditions are obtained.Then the stochastic synchronization problem of markov jumping Lur’e systems with time-varying delay is studied by means of the theory of stochastic differential equations,and the stochastic synchronization conditions are obtained in terms of LMIs.In the end,the validity and superiority of the proposed conditions are verified via two simulative examples.