scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Stability of stochastic differential equations with Markovian switching

01 Jan 1999-Stochastic Processes and their Applications (North-Holland)-Vol. 79, Iss: 1, pp 45-67
TL;DR: In this paper, the authors discuss the exponential stability of nonlinear stochastic differential equations with Markovian switching and show that the stability can be improved by using Markovians.
About: This article is published in Stochastic Processes and their Applications.The article was published on 1999-01-01 and is currently open access. It has received 714 citations till now. The article focuses on the topics: Stochastic partial differential equation & Stochastic differential equation.
Citations
More filters
Journal ArticleDOI
TL;DR: An observer-based mode-dependent control scheme is developed to stabilize the resulting overall closed-loop jump system and is utilized to eliminate the effects of sensor faults and disturbances.

514 citations

Journal ArticleDOI
TL;DR: The system discussed is the stochastic delay interval system with Markovian switching, which is a very advanced system and takes all the features of interval systems, Ito equations, and Markovians switching, as well as time lag, into account.
Abstract: In the past few years, a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with Markovian switching. However, little research has been on the stability of interval systems with Markovian switching, which is the topic of this paper. The system discussed is the stochastic delay interval system with Markovian switching. It is a very advanced system and takes all the features of interval systems, Ito equations, and Markovian switching, as well as time lag, into account. The theory developed is applicable in many different and complicated situations so the importance of the paper is clear.

493 citations

Journal ArticleDOI
TL;DR: An integral sliding mode surface and observer-based adaptive sliding mode controller is designed such that the MJSs are insensitive to all admissible uncertainties and satisfy the reaching condition and the stochastic stability of the closed-loop system can be guaranteed.

474 citations


Additional excerpts

  • ...Definition 2 (Mao, 1999)....

    [...]

Journal ArticleDOI
TL;DR: Using a supplementary variable technique and a plant transformation, a finite phase-type semi-Markov process has been transformed into a finite Markov chain, which is called its associated MarkovChain, and phase- type semi- Markovian jump systems can be equivalently expressed as its associatedMarkovianJump systems.

401 citations

Journal ArticleDOI
TL;DR: Using Liapunov functions, necessary and sufficient conditions for positive recurrence are developed and ergodicity of positive recurrent regime-switching diffusions is obtained by constructing cycles using the associated discrete-time Markov chains.
Abstract: In response to the increasing needs for control and optimization of hybrid systems, this work is concerned with such asymptotic properties as recurrence (also known as weak stochastic stability in the literature) and ergodicity of regime-switching diffusions. Using Liapunov functions, necessary and sufficient conditions for positive recurrence are developed. Then, ergodicity of positive recurrent regime-switching diffusions is obtained by constructing cycles using the associated discrete-time Markov chains.

352 citations

References
More filters
Book
01 Aug 1979
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Abstract: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of nonnegative matrices 4. Symmetric nonnegative matrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains 9. Input-output analysis in economics 10. The Linear complementarity problem 11. Supplement 1979-1993 References Index.

6,572 citations

BookDOI
01 Jan 2008
TL;DR: In this paper, the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form, are discussed, as well as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.
Abstract: This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.

3,584 citations

Book
23 Apr 1974

2,537 citations

Book
27 Nov 2012
TL;DR: In this paper, the authors present an overview of state estimates of stochastic systems with delay and their control for deterministic FEDs, including optimal control of Stochastic Delay Systems.
Abstract: Preface. 1. Models. 2. General Theory. 3. Stability of Retarded Differential Equations. 4. Stability of Neutral Type Functional Differential Equations. 5. Stability of Stochastic Functional Differential Equations. 6. Problems of Control for Deterministic FEDs. 7. Optimal Control of Stochastic Delay Systems. 8. State Estimates of Stochastic Systems with Delay. Bibliography. Index.

1,177 citations