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
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.
Proceedings ArticleDOI
H ∞ reliable control for Markovian jump systems with actuator failures and a turbofan-engine application
TL;DR: In this paper, the authors investigated the H ∞ reliable control problem for a class of Markovian jump systems with actuator failures and partly known transition rates, which may lead to less conservativeness.
Proceedings ArticleDOI
Practical control of stochastic Markovian jump systems with time-delays
TL;DR: In this article, the notions of the practical stability in probability and in the pth mean, and the practical controllability of stochastic nonlinear systems with Markovian jump parameters and time-varying delays are introduced.
Proceedings ArticleDOI
Algorithmic Analysis of Euler-Maruyama Scheme for Stochastic Differential Delay Equations with Markovian Switching and Poisson Jump, under Non-Lipschitz Condition
Guoqiang Wang,Donglong Li +1 more
TL;DR: The numerical solution converges to the true solution of stochastic differential delay equations with Poisson jump and Markovian switching in the sense of $L^{1}$-norm under one non-Lipschitz condition.
Proceedings ArticleDOI
Exponential mean-square stability of stochastic string hybrid systems
TL;DR: The sufficient conditions of exponential mean-square stability for nonlinear continuous time stochastic string hybrid systems are established and the detailed calculations are given for linear systems.
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.