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
收藏
页码：825 / 837
页数：13
相关论文
共 50 条
  • [1] Stability analysis for stochastic differential equations with infinite Markovian switchings
    Ma, Hongji
    Jia, Yingmin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 435 (01) : 593 - 605
  • [2] Stability in distribution of stochastic differential delay equations with Markovian switching
    Yuan, CG
    Zou, JZ
    Mao, XR
    SYSTEMS & CONTROL LETTERS, 2003, 50 (03) : 195 - 207
  • [3] Exponential stability of Stochastic delay differential equations with Markovian switching
    Luo, JW
    Hou, ZT
    Zou, JZ
    DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS, 2003, : 125 - 129
  • [4] On stability in distribution of stochastic differential delay equations with Markovian switching
    Nguyen Huu Du
    Nguyen Hai Dang
    Nguyen Thanh Dieu
    SYSTEMS & CONTROL LETTERS, 2014, 65 : 43 - 49
  • [5] Exponential stability of stochastic singular delay systems with general Markovian switchings
    Wang, Guoliang
    Zhang, Qingling
    Yang, Chunyu
    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2015, 25 (17) : 3478 - 3494
  • [6] Practical stability of stochastic functional differential equations with infinite delay
    Rhaima, Mohamed
    Mchiri, Lassaad
    Ben Makhlouf, Abdellatif
    Sallay, Jihen
    ASIAN JOURNAL OF CONTROL, 2024, 26 (02) : 1057 - 1067
  • [7] η-stability of hybrid neutral stochastic differential equations with infinite delay
    Caraballo, Tomas
    Mchiri, Lassaad
    Mohsen, Belfeki
    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2022, 32 (04) : 1973 - 1989
  • [8] STABILITY OF THE SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
    Chaohui Yue1
    2. School of Sciences
    Annals of Applied Mathematics, 2009, (02) : 219 - 222
  • [9] Existence and Stability for Stochastic Partial Differential Equations with Infinite Delay
    Cui, Jing
    Yan, Litan
    Sun, Xichao
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [10] Robust stability and controllability of stochastic differential delay equations with Markovian switching
    Yuan, CG
    Mao, XR
    AUTOMATICA, 2004, 40 (03) : 343 - 354
12345