A note on almost sure asymptotic stability of neutral stochastic delay differential equations with Markovian switching

被引：66

作者：

Li, Xiaoyue ^{[1
]}

Mao, Xuerong ^{[2
]}

机构：

[1] NE Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

[2] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

来源：

AUTOMATICA | 2012年 / 48卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Asymptotic stability; Neutral stochastic delay differential equations; Markov chain; Generalized Ito formula; Brownian motion; SYSTEMS;

D O I：

10.1016/j.automatica.2012.06.045

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider neutral stochastic delay differential equations with Markovian switching. Our key aim is to establish LaSalle-type stability theorems for the underlying equations. The key techniques used in this paper are the method of Lyapunov functions and the convergence theorem of nonnegative semi-martingales. The key advantage of our new results lies in the fact that our results can be applied to more general non-autonomous equations. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：2329 / 2334

页数：6

共 20 条

[1]

[Anonymous], 1960, PRIKLAD MATI MEKHAN

[2]

[Anonymous], 1998, Method of Lyapunov functions in problems of stability and stabilization of systems of stochastic structure

[3]

[Anonymous], 2007, STOCHASTIC DIFFERENT

[4] Convergence rate of numerical solutions to SFDEs with jumps [J].

Bao, Jianhai ;

Boettcher, Bjoern ;

Mao, Xuerong ;

Yuan, Chenggui .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 236 (02) :119-131

[5] Stability of Singular Stochastic Systems With Markovian Switching [J].

Huang, Lirong ;

Mao, Xuerong .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2011, 56 (02) :424-429

[6] On Almost Sure Stability of Hybrid Stochastic Systems With Mode-Dependent Interval Delays [J].

Huang, Lirong ;

Mao, Xuerong .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (08) :1946-1952

[7] Neutral stochastic differential delay equations with Markovian switching [J].

Kolmanovskii, V ;

Koroleva, N ;

Maizenberg, T ;

Mao, X ;

Matasov, A .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2003, 21 (04) :819-847

[8]

Kolmanovskii V.B., 1981, STABILITY PERIODIC M

[9]

Ma Z., 2006, NE MATH J, V22, P479

[10]

Mao X., 2006, STOCHASTIC DIFFERENT, DOI [10.1142/p473, DOI 10.1142/P473]

← 1 2 →