Stabilization of stochastic coupled systems with Lévy noise and regime switching diffusions via intermittent control with a time delay

In this paper, the stabilization problem of stochastic Lévy noise coupled systems with time delays and regime switching diffusions (SLCSTR) is researched via intermittent control with a time delay (ICTD). It is worth pointing out that both Lévy noise and regime switching diffusions are considered into coupled systems. Furthermore, different from previous intermittent control based on current state, ICTD combining the benefits of aperiodically intermittent control and delay feedback control is based on past state. Meanwhile, the stabilization problem of SLCSTR is investigated via delay feedback control. Then, by Lyapunov method, graph theory and some techniques of inequalities, some stabilization criteria of SLCSTR in the sense of exponential stability in mean square are obtained. In addition, we investigate the stabilization problem of stochastic delayed coupled oscillators with Lévy noise and regime switching diffusions as a practical application of our theoretical results. Finally, numerical simulations are given for illustration.