Stochastically asymptotic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances

In this paper we study stochastic stability of delayed recurrent neural networks with both Markovian jump parameters and nonlinear disturbances. Based on the Lyapunov stability theory, the properties of a Brownian motion, the generalized Itô's formula and linear matrix inequalities technique, some new delay-dependent conditions are derived to guarantee the stochastically asymptotic stability of the trivial solution or zero solution. In particular, the activation functions in this paper depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. Also, time delays proposed in this paper comprise both constant delays and time-varying delays. Moreover, the derivative of time delays is allowed to take any value. Therefore, the results obtained in this paper are less conservatism and generalize those given in the previous literature. Finally, two numerical examples and their simulations are used to show the effectiveness of the obtained results.