Stability of stochastic functional differential equations with impulses by an average approach. (August 2018)

• Record Type: Journal Article
• Authors: Li, Bing
• Is Part Of: Nonlinear analysis. Volume 29(2018)
• Page Start: 221
• Page End: 233
• Publication Date: 2018-08
• Subjects: Impulsive stochastic system -- Average impulsive interval -- Stability -- Stabilization; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2018.02.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper is concerned with the stability issues of stochastic functional differential equations with impulsive effects. Several unified Lyapunov-type stability criteria are established based on the formula of the variation of parameters and the comparison principle of the impulsive systems. The sufficient conditions proposed in this paper depend mainly on the integral average value of the time-varying coefficients and the average impulsive interval, which are less conservative than previous literature. Two examples are provided to demonstrate the effectiveness of the theoretical results. Highlights: Novel criteria are derived for the stability and stabilization. Restrictions on diffusion operator have been weakened. The average value of integral for coefficients is involved. The average impulsive interval is employed.