Robust Stability of Markovian Jump Stochastic Neural Networks with Time Delays in the Leakage Terms

Abstract

This paper deals with the problem of exponential stability for a class of Markovian jump stochastic neural networks with time delays in the leakage terms and mixed time delays. The jumping parameters are modeled as a continuous-time, finite-state Markov chain, and the mixed time delays consist of time-varying delays and distributed delays. By using the method of model transformation, Lyapunov stability theory, stochastic analysis and linear matrix inequalities techniques, several novel sufficient conditions are derived to guarantee the exponential stability in the mean square of the equilibrium point of the suggested system in two cases: with known or unknown parameters. Moreover, some remarks and discussions are given to illustrate that the obtained results are significant, which comprises and generalizes those obtained in the previous literature. In particular, the obtained stability conditions are delay-dependent, which depends on all the delay constants, and thus the presented results are less conservatism. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.