Stability for multi-links stochastic delayed complex networks with semi-Markov jump under hybrid multi-delay impulsive control

This paper is concerned with the problem of pth moment exponential stability for multi-links stochastic delayed complex networks with semi-Markov jump under hybrid multi-delay impulsive control. Different from the previous literature on multi-links systems, we take semi-Markov jump into account. The hybrid multi-delay impulses we addressed are composed of unstable delay-free impulses, stable delay-free impulses, unstable multi-delay impulses and stable multi-delay impulses. Average multi-delay impulsive gain is proposed to quantify the strength of the impulses. Serving as an extension of Halanay inequality, a novel multi-delay impulsive differential inequality is constructed. Combining the multi-delay impulsive differential inequality with Lyapunov method and graph theory, the sufficient criteria for pth moment exponential stability of the considered systems are given, which are closely related to average multi-delay impulsive gain, topological structure, stochastic disturbance strength and semi-Markov jump. Furthermore, the obtained theoretical results are applied to a class of stochastic delayed coupled oscillator systems. Finally, a corresponding numerical simulation is provided to demonstrate the effectiveness of the proposed theoretical results.