Discrete Stochastic Absolute Stability Of Lurie Systems And Neural Network Synchronization

In this thesis , the robust absolute stability of discrete-time stochastic Lurie system and the synchronization of couple neural networks is investigated. By using the Lyapunov stability theory, Stochastic analysis theory, Gronwall-Bellman inequality, Schur complement, matrix inequality and so on. we establish the delay-dependent sufficient conditions of the discrete-time stochastic Lurie system. We employ the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the global asymptotically synchronization of the addressed delay networks. Which include the following content:The first, the robust absolute stability of discrete-time stochastic Lurie system is investigated, the discrete-time stochastic Lurie system is an important class of uncertain nonlinear systems. Robust stability have been a number of subjects of general interest. We construct a number of Lyapunov-Krasovkii functions, again supporting the right upper derivative of Lyapunov-Krasovkii functions , by adding a number of zero matrices ,and by using linear matrix inequality (LMI) method ,we established the robust sbsolute conditions of the discrete-time stochastic Lurie system. Because of the condition consists of lots of free matrices ,so the condition has the less conservative .A numerical example illustrates the effectiveness.The second, by utilizing the norm inequalities and the properties of Kronecker product , we investigates the synchronization of synchronization of uncertain coupled neural network with time-varying delays. By constructing an appropriate Lyapunov- Krasovkii function, a new delay-dedpendent criterion for the synchronization is established in terms of linear matrix inequalities(LMIS).By using LMI toolbox in MATLAB, A numerical example illustrates the effectiveness.