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
Nonfragile controller design for linear Markovian jumping parameters systems
TL;DR: In this paper, a nonfragile robust controller for continuous-time linear systems with Markovian jumping parameters is proposed when the uncertainties in the system matrices are of the norm-bounded type.
Journal ArticleDOI
New Criteria on Delay-Dependent Robust Stability for Uncertain Markovian Stochastic Delayed Neural Networks
TL;DR: Some new delay-dependent stability criteria are established for the considered systems by constructing a modified Lyapunov–rasovskii functional, which are expressed in terms of linear matrix inequalities.
Proceedings ArticleDOI
Randomly switching systems: Models, analysis, and applications
TL;DR: In this article, the authors provide a survey on the recent progress of switching diffusion systems and their application in a variety of applications, and provide a useful tool to replace the time-varying system measures by an ergodic or limit measure.
Journal ArticleDOI
Robust H∞ filtering for finite-time boundedness of Markovian jump system with distributed time-varying delays
TL;DR: A novel delay-dependent criterion is presented such that the error system is stochastically finite-time bounded and the filter matrix can be achieved by solving the linear matrix inequalities (LMIs).
Journal ArticleDOI
Necessary and sufficient conditions for ergodicity of CIR type SDEs with Markov switching
TL;DR: In this paper, the Cox-Ingersoll-Ross (CIR) interest rate model with Markov switching was considered and the ergodicity and transience of the CIR model was 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
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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.
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.