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Stability of Stochastic Functional Differential Systems with Semi-Markovian Switching and Lévy Noise and Its Application

Wenpin Luo, Xinzhi Liu, and Jun Yang*
International Journal of Control, Automation, and Systems, vol. 18, no. 3, pp.708-718, 2020

Abstract : This paper investigates the general decay stability on systems represented by stochastic functional differential equations with semi-Markovian switching and Lévy noise (SFDEs-sMS-LN). Based on generalized multidimensional Itô’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 Lévy 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.

Keyword : Binary diagonal matrix (BDMs), Lévy noise, semi-Markovian systems, stochastic functional differential equation (SFDEs), vertex approach.

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