Stabilization of stochastic delayed networks with Markovian switching and hybrid nonlinear coupling via aperiodically intermittent control

Abstract This paper concerns the stabilization problem of stochastic delayed networks with Markovian switching and hybrid coupling (SDNMH) via aperiodically intermittent control. Compared with the existing works on hybrid coupling, the hybrid coupling in this paper can be nonlinear, which is more general. By establishing a new differential inequality on delayed dynamical systems with Markovian switching, the stabilization problem of SDNMH via aperiodically intermittent control is studied. By means of Lyapunov method and graph-theoretic technique, two kinds of sufficient criteria are given. The derived results are closely related to the topology structure of the underlying network, the transition rate of Markov chain, the maximum proportion of rest time and the control gain. Finally, the theoretical results are tested by a class of coupled oscillators networks with Markovian switching and hybrid coupling.

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