Delay-dependent stability of highly nonlinear hybrid stochastic systems with Levy noise

Abstract

In this paper, we focus our study on a class of hybrid Stochastic Differential Delay Equations with Levy Noise (hybrid SDDE-LN), when the drift coefficient, the diffusion coefficient, and the jump coefficient satisfy the locally Lipschitz condition and the general monotonicity condition. By using the Lyapunov function approach, the Barbalat Lemma, and stochastic calculus, some criteria are established to guarantee the delay-dependent stability, as $H_{\infty}$-stability in $L^{p}$ and asymptotic stability in $L^{p}$. Finally, a numerical example illustrates the main theoretical results.