Abstract
Lévy noise has been employed to stabilize the hybrid differential system, which has generalized the Brownian motion case. We divide the state space of Markov chain into two subsets, which are regarded as the modes, and deal with the unobservable part of hybrid system. The sufficient conditions of stabilization and destabilization have been given in the main results, and we discuss the reasons of increasing conservatism in the final section of the paper.
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