Sliding-mode synchronization for nonidentical Markovian jump neural networks with leakage delay and partially unknown transition probabilities

This paper deals with an integral sliding mode control design for synchronization of two nonidentical Markovian jump neural networks with leakage delay, discrete time-varying delays and partially unknown transition probabilities. Based on a mode-dependent Lyapunov-Krasovskii functional combined with Finsler´s lemma, delay-dependent conditions guaranteeing the mean-square exponential stability of the synchronization error dynamics in sliding mode are derived in terms of linear matrix inequalities. Then, a sliding mode synchronization controller is designed such that the synchronization error system´s trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.