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
More filters
Posted Content
Exponential stability of the exact solutions and $\theta$-EM approximations to neutral SDDEs with Markov switching
Guangqiang Lan,Chenggui Yuan +1 more
TL;DR: Sufficient conditions are obtained to ensure the p th moment and almost sure exponential stability of the exact solutions as well as ?
Journal ArticleDOI
Observer Design for Descriptor Markovian Jumping Systems with Nonlinear Perturbations
TL;DR: In this paper, the observer design problem for a class of descriptor Markovian jumping systems with nonlinear perturbations is addressed, and sufficient conditions for the existence of both full-order and reduced-order observers are given, which are equivalent to a set of linear matrix inequalities.
Journal ArticleDOI
On the approximations of solutions to neutral SDEs with Markovian switching and jumps under non-Lipschitz conditions
Wei Mao,Xuerong Mao +1 more
TL;DR: The Euler approximate solutions for NSDEwMSJs are presented and it is shown that the convergence of the Euler approximation solutions to the true solutions by applying It o ^ formula, Bihari’s lemma and Burkholder–Davis–Gundy's lemma.
Journal ArticleDOI
Passive control synthesis for uncertain markovian jump systems with multiple mode-dependent time-delays
TL;DR: In this paper, the robust passivity synthesis problem for uncertain Markovian jump systems with multiple mode-dependent time delays is addressed, and sufficient conditions for passivity are obtained in terms of linear matrix inequalities.
Journal ArticleDOI
Observer-based finite-time stabilization for extended Markov jump systems
Xiaoli Luan,Fei Liu,Peng Shi +2 more
TL;DR: In this article, the authors studied the problem of observer-based finite-time stabilization for a class of extended Markov jump systems with norm-bounded uncertainty and external disturbances.
References
More filters
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.