Stability of stochastic functional differential systems with semi-Markovian switching and Lévy noise by functional Itô’s formula and its applications

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 functional Ito’s formula, multiple degenerate Lyapunov functionals and nonnegative semi-martingale convergence theorem, new pth moment and almost surely stability criteria with general decay rate for SFDEs-SMS-LN are established. Meanwhile, the diffusion operators are allowed to be controlled by multiple auxiliary functions with time-varying coefficients, which can be more adaptable to the non-autonomous SFDEs-SMS-LN with high-order nonlinear coefficients. Furthermore, as applications of the presented stability criteria, new delay-dependent sufficient conditions for general decay stability of the stochastic delayed neural network with semi-Markovian switching and Levy noise (SDNN-SMS-LN) and the scalar non-autonomous SFDE-SMS-LN with non-global Lipschitz condition are respectively obtained in terms of binary diagonal matrices (BDMs) and linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the effectiveness of the proposed results.