Stabilization of multi-group models with multiple dispersal and stochastic perturbation via feedback control based on discrete-time state observations

Abstract This paper focuses on the multi-group models with multiple dispersal and stochastic perturbation (MGMDS). The effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration. The stabilization of MGMDS is investigated via feedback control based on the discrete-time state observations. In addition, a systematic method is given to construct a global Lyapunov function for MGMDS. By means of graph theory and Lyapunov method, some sufficient conditions are obtained to ensure the stabilization in the sense of mean-square asymptotical stability. An upper bound of the duration between two consecutive state observations is estimated. Moreover, to show the applicability of our results, the main theory is employed to a stochastic coupled oscillators. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results.

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