Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates

In this paper, finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates. By constructing the suitable stochastic Lyapunov-Krasovskii functional, using finite-time stability theorem, inequality techniques and the pinning control technique, several sufficient criteria have been proposed to ensure the finite-time synchronization for the MJCNs with or without time delays. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, this paper has important theory significance and practical application value. Finally, numerical simulations illustrated by mode jumping from one mode to another according to a Markovian chain with partially unknown transition probability verify the effectiveness of the proposed results.