Stability of stochastic differential equations with Markovian switching
TLDR
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.read more
Citations
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Journal ArticleDOI
Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate
TL;DR: In this paper , a stochastic hepatitis B epidemic model with saturated incidence rate, which is perturbed by both white noise and colored noise, was investigated and sufficient criteria for extinction of the disease were derived.
Journal ArticleDOI
Robust adaptive stabilization by high gain feedback for Markovian jump systems with partially unknown transition rates
TL;DR: In this paper, a universal adaptive high gain controller is proposed for a class of nonlinear perturbed Markovian jump systems with partially unknown transition rates, and the convergence and boundedness of the closed-loop system signals in the mean square sense are ensured.
Proceedings ArticleDOI
Stability of jump diffusions with random switching
Gang George Yin,Fubao Xi +1 more
TL;DR: This paper focuses on the long-time behavior, namely, stability of the switching jump diffusions, and uses a transformation technique to obtain a necessary and sufficient condition for stability.
Proceedings ArticleDOI
Output feedback stabilization of stochastic linear systems with Markovian switching and uncertain transition jump rates
TL;DR: In this article, the authors investigated the problem of output feedback stabilization for a class of stochastic linear systems with Markovian switching and uncertain transition jump rates and provided a sufficient condition in terms of linear matrix inequalities (LMIs) such that the closed-loop system is stochastically asymptotically stable in the large.
Journal ArticleDOI
Robust Stability Analysis of Linear Parameter-Varying Systems With Markov Jumps
TL;DR: In this paper , the mean-square stability of linear parameter-varying systems with Markov jumps is investigated, where the model dynamics are driven not only by a Markov chain but also by time varying parameters that take values in a polytopic set, and the stability certificate is sought through linear matrix inequalities.
References
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Book
Nonnegative Matrices in the Mathematical Sciences
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
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Stochastic differential equations and applications
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.
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Applied Theory of Functional Differential Equations
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.