Almost sure stability with general decay rate of neutral stochastic delayed hybrid systems with Lévy noise

Abstract This paper focuses on neutral stochastic delayed hybrid systems with Levy noise (NSDHSs-LN). A kind of ψ -function is introduced and the almost sure stability with general decay rate is investigated, including the exponential stability and the polynomial stability. By virtue of Lyapunov function and nonnegative semi-martingale convergence theorem, we propose sufficient conditions for the almost sure stability of the NSDHSs-LN. Moreover, we give an upper bound of each coefficient at any mode according to the theory of M-matrix. Especially, the coefficients of considered systems can be allowed to be high order nonlinear. Finally, two examples are given to show the effectiveness of our results.

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