Almost sure stability with general decay rate of neutral stochastic delayed hybrid systems with Lévy noise. (May 2017)

• Record Type: Journal Article
• Authors: Li, Mengling; Deng, Feiqi
• Is Part Of: Nonlinear analysis. Volume 24(2017)
• Page Start: 171
• Page End: 185
• Publication Date: 2017-05
• Subjects: ψ-function -- Neutral stochastic delayed hybrid systems -- Lévy noise -- Nonnegative semi-martingale convergence theorem -- M-matrix; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2017.01.001
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper focuses on neutral stochastic delayed hybrid systems with Lévy 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.