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
Mean-Square Stability of Two-Time Scale Linear Stochastic Hybrid Systems
Ewelina Seroka,Lesław Socha +1 more
TL;DR: In this paper, the problem of exponential mean-square stability of two-time scale, linear stochastic hybrid systems has been studied and two basic approaches of stability analysis for one-time hybrid systems with a Markovian switching rule and any switching rule, and singularly perturbed nonhybrid systems were combined.
Posted Content
Exponential ergodicity and steady-state approximations for a class of Markov processes under fast regime switching
TL;DR: In this paper, the ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching were studied. And the convergence rates for the moments of the approximating diffusion process to those of the Markov modulated birthdeath process were established by comparing the generator of the approximate diffusion and that of the joint Markov process.
Proceedings ArticleDOI
Mean square exponential stability of uncertain linear impulsive stochastic systems with Markovian switching
TL;DR: In this article, the authors considered mean square exponential stability of uncertain linear impulsive systems with Markovian switching and derived sufficient conditions for the stability of these systems, which depend on both on the lower bound and the upper bound of impulse intervals.
Journal ArticleDOI
Stability and positivity with respect to part of the variables for positive Markovian jump systems
Journal ArticleDOI
Stabilisation of hybrid system with different structures by feedback control based on discrete-time state observations
Banban Shi,Xuerong Mao,Fu Ke Wu +2 more
TL;DR: In this paper , a discrete-time feedback control for hybrid stochastic differential equations (SDEs) with different structures in different modes is proposed, where the coefficients of the SDEs satisfy the linear growth condition, while in the other modes, the coefficients are highly nonlinear.
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.