Stability of a class of neutral stochastic functional differential equations with Markovian switching

被引：16

作者：

Song, Ruili ^{[1
,2
,3
]}

Lu, Boliang ^{[3
]}

Zhu, Quanxin ^{[1
,2
,4
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Nanjing Normal Univ, Inst Finance & Stat, Nanjing 210023, Jiangsu, Peoples R China

[3] Nanjing Univ Finance & Econ, Sch Appl Math, Nanjing 210023, Jiangsu, Peoples R China

[4] Hunan Normal Univ, Coll Math & Stat, Key Lab HPC SIP MOE, Changsha 410081, Hunan, Peoples R China

来源：

IET CONTROL THEORY AND APPLICATIONS | 2018年 / 12卷 / 15期

基金：

中国国家自然科学基金;

关键词：

stability criteria; Markov processes; Lyapunov methods; convergence; stochastic systems; differential equations; asymptotic stability; stochastic processes; neutral stochastic functional differential equations; Markovian switching; multiple Lyapunov functions; essential neutral term; multiple auxiliary functions; pth moment exponential stability; almost sure exponential stability; generalised Ito formula; nonnegative semi-martingale convergence theorem; constant coefficients; time-varying coefficients; TIME-VARYING DELAYS; RAZUMIKHIN-TYPE THEOREMS; EXPONENTIAL STABILITY; NEURAL-NETWORKS; ASYMPTOTIC STABILITY; UNBOUNDED DELAY; INFINITE DELAY; BOUNDEDNESS; SYNCHRONIZATION; EXISTENCE;

D O I：

10.1049/iet-cta.2017.0806

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This study investigates the stability of a class of neutral stochastic functional differential equations with Markovian switching. Some novel stability criteria are first established, including boundedness, pth moment exponential stability and almost sure exponential stability, based on multiple Lyapunov functions, generalised Ito formula and non-negative semi-martingale convergence theorem. Concretely, the authors generalise the existing results under the essential neutral term and improve the diffusion operators from being controlled by two auxiliary functions to other multiple auxiliary functions with not only constant coefficients but also time-varying coefficients. Some numerical examples are presented to illustrate the effectiveness of the obtained results.

引用

页码：2043 / 2054

页数：12

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