Stability Of Delay Stochastic Neural Network

Robust stochastic stability problem of uncertain stochastic neural networks witha time-varying delay and robust stochastic stabilization problem of uncertain s-tochastic neural networks with mixed delays are mainly studied in this thesis.First, we consider the robust stochastic stability problem of uncertain stochas-tic neural networks with a time-varying delay. Based on model transformation, byconstructing a suitable Lyapunov function and using the Jensen inequality methoda sufcient condition ensuring robust stochastic stability of delayed uncertain s-tochastic neural network is given in the form of linear matrix inequation (LMI). Anumerical example illustrates that the method proposed here is less conservativethan one in [IEEE Transactions on Neural Networks,2010,21(3);1-15].Second, we consider the robust stochastic stabilization problem of uncertainstochastic neural networks with mixed delays. Due to Lyapunov-Krasovskii func-tional and stochastic stability theory, a designing method of state feedback controlleris proposed by using It o formulation and inequality technique. Sufcient conditionsin the form of nonlinear matrix inequalities, under which the system is robustlyasymptotically mean square stable and can be stochastically stabilized, are estab-lished. Furthermore, we design a cone complementary linearization algorithm, whichtransforms the problem of solving a nonlinear matrix inequality into one that solvinga linear matrix inequality, and thereby a state feedback controller which makes theresultant closed-loop system mean suqare asymptotically stable is obtained. Finally,a numerical example and its simulation are given to illustrate the efciency of theproposed method.