Stochastic Differential Delay Equations with Markovian Switching

Mao, Xuerong; Matasov, A. I.; Piunovskiy, Alexey

doi:10.2307/3318634

Cited by 190 publications

(131 citation statements)

References 13 publications

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“…Mao (1999) investigated the exponential stability for general nonlinear stochastic di erential equations with Markovian switching dX (t) = f(X (t); t; r(t)) dt + g(X (t); t; r(t)) dB(t): (1.2) Shaikhet (1996) took the time delay into account and considered the stability of a semi-linear stochastic di erential delay equation with Markovian switching, while Mao et al (2000) investigated the stability of a nonlinear stochastic di erential delay equation with Markovian switching. Most of these papers are concerned with asymptotic stability in probability or in mean square (i.e.…”

Section: Introductionmentioning

confidence: 99%

Stability in distribution of stochastic differential delay equations with Markovian switching

Chen

Zou

Mao

2003

Systems & Control Letters

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Section: Introductionmentioning

confidence: 99%

Stability in distribution of stochastic differential delay equations with Markovian switching

Chen

Zou

Mao

2003

Systems & Control Letters

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“…By the results of [5], system (32) are exponentially stable and asymptotically stable in mean square if the upper bound of time delay h max < 0.3996 and h max < 0.4127 respectively. However, by Theorem 1, system (32) is exponentially stable when h ≤ 0.6411, which is much less conservative.…”

Section: Dx(t) = [A(r(t))x(t)+b(r(t))x(t−h)]dt+σ(r(t))x(t−h)dw(t) mentioning

confidence: 99%

“…These works can be classified into two categories according to their dependence on the information about the size of time delays of the system, say, they are either delayindependent results ( [6], [8], [9] and [16]) or delaydependent criteria ( [5], [7], [9] and [17]). Generally, for the cases of small delays, delay-independent results are more conservative than those dependent on the size of delays.…”

Section: X(t) = A(r(t))x(t) mentioning

confidence: 99%

Delay-dependent robust stability of stochastic delay systems with Markovian switching

Huang

Mao

Deng

2009

J. Control Theory Appl.

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This version is available at https://strathprints.strath.ac.uk/16872/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Abstract: In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

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“…Moreover, it is usually difficult to obtain accurate values for the delay and conservative estimates often have to be used. The importance of time delay has already motivated several studies on the stability of switching diffusions with time delay, see, for example, [8,11,13].…”

Section: Introductionmentioning

confidence: 99%

Comparison theorem of one-dimensional stochastic hybrid delay systems

Yang

Mao

Chen

2008

Systems & Control Letters

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This version is available at https://strathprints.strath.ac.uk/13802/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. AbstractIn this paper, the comparison theorem of stochastic differential delay equations with Markovian switching has been investigated. In order to develop our theory, a new proof of existence and uniqueness of stochastic differential equations with Markovian switching is given.

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Stochastic Differential Delay Equations with Markovian Switching

Cited by 190 publications

References 13 publications

Stability in distribution of stochastic differential delay equations with Markovian switching

Stability in distribution of stochastic differential delay equations with Markovian switching

Delay-dependent robust stability of stochastic delay systems with Markovian switching

Comparison theorem of one-dimensional stochastic hybrid delay systems

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