Hybrid multi-delay impulsive control for synchronisation of multi-links stochastic delayed complex networks with semi-Markov jump

Abstract

In this paper, synchronisation between multi-links stochastic delayed drive complex networks with semi-Markov jump and the corresponding response networks via hybrid multi-delay impulsive control is researched. Thereinto, the hybrid multi-delay impulses include synchronous and asynchronous impulses without delay, synchronous impulses and asynchronous with multi delays. We put up with a concept of average multi-delay impulsive gain to quantify the impulses effects. A novel multi-delay impulsive differential inequality is also established. Utilizing it, combining with Lyapunov method and graph theory, we provide two sufficient criteria to make the drive networks and the corresponding response networks achieve exponential synchronisation which are closely related to the average multi-delay impulsive gain, semi-Markov jump, multi links and stochastic disturbance. Then we apply the theoretical results into a class of stochastic delayed oscillators networks and a numerical example is presented to illustrate the validity of our theoretical results.