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
Stability of singularly perturbed nonlinear stochastic hybrid systems
TL;DR: In this paper, the problem of exponential mean-square stability of nonlinear singularly perturbed, stochastic hybrid systems is studied and two basic approaches of stability analysis for hybrid systems with a given Markovian switching rule and any Markovians switching rule were combined.
Journal ArticleDOI
Distributed finite-time stochastic control for spatially interconnected Markovian jump systems
TL;DR: The formulation of distributed stochastic controllers is developed such that the corresponding closed-loop spatially interconnected Markovian jump systems are well-posed, finite-time Stochastic stable/bounded and finite- Time-Finite Stochastic contractive.
Proceedings ArticleDOI
Decentralized stabilization of Markovian jump large-scale systems via neighboring mode dependent output feedback control
Shan Ma,Junlin Xiong +1 more
TL;DR: A sufficient condition is given in terms of rank constrained linear matrix inequalities (rank constrained LMIs) for the design of local controllers in a class of uncertain Markovian jump large-scale systems.
Book ChapterDOI
Suppression of functional system with Markovian switching
Lizhu Feng,Yi Shen,Zhuguo Li +2 more
TL;DR: A class of functional system whose coefficient satisfies the local Lipschitz condition and the one-sided polynomial growth condition under Markovian switching is investigated.
Journal ArticleDOI
Smooth densities for SDEs driven by subordinated Brownian motion with Markovian switching
Xiaobin Sun,Yingchao Xie +1 more
TL;DR: In this article, a class of stochastic differential equations driven by subordinated Brownian motion with Markovian switching is considered and the smoothness of the density for the solution under uniform Hormander type condition is investigated.
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
BookDOI
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.
Book
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.