Abstract
The almost sure exponential stabilization and pth moment exponential stabilization for hybrid stochastic system (HSS) with control input delay, Lévy noise and asynchronous switching will be studied in this paper. Adequate conditions will be built to ensure the pth moment stability for the HSS which refer to the sizes of the delays by taking full advantage of Lyapunov functional approach. We investigate the almost sure exponential stability standard of nominal systems by using compound Lyapunov function method with modal dependence. In addition, we further study the almost sure exponential stability for HSS with Lévy noise and delayed feedback controller according to the comparison principle for sufficiently small delays as long as the nominal system is almost surely exponentially stable. An example and some simulations will propose to illustrate the results.
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