Improved Stabilization Results for Markovian Switching CVNNs with Partly Unknown Transition Rates

Abstract

In this paper, stochastic stability and stabilization problems are investigated for the Markovian switching complex-valued neural networks with mixed delays, where the transition rates (TRs) of the Markov chain are partly unknown, which might reflect more the realistic dynamical behaviors of the neural networks. On the basis of the Lyapunov stability theory and the stochastic analysis method as well as the properties of the TR matrix, several mode-dependent criteria are derived to guarantee the considered complex-valued network to be globally asymptotically stable in mean-square sense. Then, by proposing an appropriate mode-dependent controller, stabilization conditions in terms of matrix inequalities are derived to guarantee the closed-loop system to be stochastically mean-square stable. Finally, two simulation examples are presented to illustrate the effectiveness of the proposed theoretical results.