Synchronization And Stability Analysis For Stochastic Markovian Jump Systems

Since the introduction of chaos control and synchronization,a lot of research results have been obtained,and theses researches have high theoretical and practical values.It has been widely applied to different fields such as chemistry,biology,electronics and informatics;The Markovian jump systems belong to the stochastic hybrid systems.Since the 1990s,due to the development of mathematical theory and computer,more and more scholars have begun to study the Markovian jump system,and its results have been widely used in aerospace,communications and other fields.In this paper,robustly adaptive synchronization for stochastic Markovian neural networks of neutral type with mixed mode-dependent delays and exponential stability in mean square for Markovian jump memristive neural networks with mode-dependent delays and partially unknown transition probabilities are studied.The main contents of this paper are summarized as follows:The first chapter is the introduction part,which mainly expounds the research background,progress and purpose of the synchronization problem of chaotic systems,Markovian jump system,and introduces the main work and symbolic description of this paper.In the second chapter,a robust adaptive feedback controller is designed to achieve complete synchronization of a class of neutral-type stochastic Markovian jump neural networks with mode-dependent and mixed delays.The mixed delays consist of time-varying discrete delays and continuously distributed delays.By employing Wirtinger-based integral inequality,a reciprocally convex combination technique and a generalized LaSalle-type invariance principle for stochastic Markovian differential delay equations,a globally almost surely asymptotical stability condition of the error dynamical system in the mean-square sense is established for all admissible uncertainties.An example and its numerical simulation are given to demonstrate the effectiveness of the theoretical results.In the third chapter,we study the exponential stability in mean square problem of a class of Markovian jump memristive neural networks with partial transition probabilities unknown and mode-dependent delays.The delays vary randomly according to the Markov mode in this chapter.Each of the transition probabilities may be known to have its estimated value and upper and lower bounds,or may be completely unknown.By using a new Lyapunov-Krasovskii functional,we derive a delay-dependent stability criterion,which can be expressed in terms of a set of linear matrix inequalities.