Robust Synchronization of Stochastic Markovian Jumping CVNs with Randomly Occurring Nonlinearities and Generally Uncertain Transition Rates

This article intents to the robust synchronization issue for Markovian jumping complex-valued networks (CVNs) subject to the stochastic noises and randomly occurring nonlinearities, where the considered transition rates are generally uncertain, which expands the existed relevant results. Meanwhile, two random variables with pre-given statistical characteristics are proposed to explain the involved randomly occurring nonlinearities phenomenon, and random variables are mutually independent. By designing the appropriate mode-dependent controller, combined with generalized complex It \(\hat{o}\) $\widehat{o}$ ’s formula, Lyapunov stability theory, and the properties of the transition rate matrix, some sufficient conditions are achieved to ensure error system realizes stochastically asymptotically mean-square stable. Furthermore, sufficient mode/delay-dependent criteria of globally exponential synchronization for considered CVNs are also investigated. In the end, two illustrative examples with simulations are proposed to verify the effectiveness and feasibility of the designed control schemes.