Stochastic stability of fractional-order Markovian jumping complex-valued neural networks with time-varying delays

This paper is concerned with the problem of stochastic stability analysis for fractional-order Markovian jumping complex-valued neural networks (MJCVNNs) with time-varying delays. The novelty of this study is emphasized in two phases. In first phase, MJCVNNs is considered in the form of fractional-order systems. Secondly, complex-valued Wirtinger based integral inequality is newly constructed. The existence and uniqueness conditions of the proposed systems are derived based on the homeomorphism theorem in the complex domain. Then, the stochastic stability condition is derived in terms of linear matrix inequalities (LMIs) for the MJCVNNs by employing Lyapunov indirect method. The feasibility of the derived conditions is verified by the numerical examples and their simulation results are demonstrated to show the effectiveness of the fractional-order derivatives and proposed approach.