Abstract
This paper investigates the general decay stability on systems represented by stochastic functional differential equations with semi-Markovian switching and Levy noise (SFDEs-sMS-LN). Based on generalized multidimensional Ito’s formula and multiple Lyapunov functions, a new pth moment stability criterion with general decay rate is established. Meanwhile, as an applications of the presented stability criterion, we consider the stabilization problem of stochastic delayed neural networks with semi-Markovian switching and Levy noise (SDNN-sMS-LN). A vertex approach is proposed to design the controller in terms of binary diagonal matrices (BDMs) and linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.
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