Stability of linear stochastic delay differential equations with infinite Markovian switchings

被引：40

作者：

Song, Ruili ^{[1
,2
,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] Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany

来源：

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL | 2018年 / 28卷 / 03期

基金：

中国国家自然科学基金;

关键词：

asymptotic mean square stability; exponential mean square stability with conditioning; infinite Markovian switchings; stochastic delay differential equation; stochastic stability; WHITE-NOISE PERTURBATIONS; JUMP PARAMETER-SYSTEMS; MEAN-SQUARE STABILITY; EXPONENTIAL STABILITY; TIME DELAYS; MODEL; NETWORKS; FEEDBACK;

D O I：

10.1002/rnc.3905

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 paper investigates the stability of linear stochastic delay differential equations with infinite Markovian switchings. Some novel exponential stability criteria are first established based on the generalized Ito formula and linear matrix inequalities. Then, a new sufficient condition is proposed for the equivalence of 4 stability definitions, namely, asymptotic mean square stability, stochastic stability, exponential mean square stability with conditioning, and exponential mean square stability. In particular, our results generalize and improve some of the previous results. Finally, two examples are given to illustrate the effectiveness of the proposed results.

引用

页码：825 / 837

页数：13

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