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
Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates
TL;DR: Finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates by constructing the suitable stochastic Lyapunov–Krasovskii functional using finite-time stability theorem, inequality techniques and the pinning control technique.
Journal ArticleDOI
Stability in distribution of stochastic differential delay equations with Markovian switching
TL;DR: Stochastic differential delay equations with Markovian switching is discussed to investigate the stability in distribution of the equations.
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Letters: Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters
Shuping He,Fei Liu +1 more
TL;DR: The stochastic finite-time boundedness (FTB) problem is considered for a class of Markovian jumping neural networks (MJNNs) with time delay and uncertainties by selecting the appropriate Stochastic Lyapunov-Krasovskii functional.
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Asynchronous Finite-Time Filtering of Markov Jump Nonlinear Systems and Its Applications
TL;DR: In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate by resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques.
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Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities
Shuping He,Shuping He,Fei Liu +2 more
TL;DR: In this article, the stochastic finite-time boundedness problem for uncertain Markovian jumping neural networks (MJNNs) is considered and sufficient conditions of stochastically finite time boundedness of MJNNs are presented and proved.
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.