Global asymptotic stability of random nonlinear switching and impulsive systems

In this paper, the concept of global asymptotic stability in probability (GAS-P) is investigated for a class of nonlinear switching and impulsive systems with random disturbances, whose second-order moments are finite. Using average switching and impulsive interval approach, we show that when the average interval is large enough, a switching and impulsive system is GAS-P if all of its constituent subsystems are GAS-P. Furthermore, if some of the constituent subsystems are not GAS-P, it is shown that the GAS-P can still be established for the system, if the non-GAS-P subsystems are not activated too long. Finally, an illustrative example are presented to demonstrate the theoretical findings.

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