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
H∞ mode-dependent fault detection filter design for stochastic Markovian jump systems with time-varying delays and parameter uncertainties.
TL;DR: This paper deals with the problem of robust H∞ fault detection for a class of stochastic Markovian jump systems (SMJSs) by using Lyapunov stability theory and generalized Itô formula, and some novel mode-dependent and delay-dependent sufficient conditions in terms of linear matrix inequality (LMI).
Journal ArticleDOI
Stabilization of stochastic delayed neural networks with markovian switching
Yonghui Sun,Jinde Cao +1 more
TL;DR: In this paper, the authors investigated the mean square exponential stabilization problem for a class of stochastic delayed neural networks with Markovian switching and proposed several stabilization criteria, delay-independent and delay-dependent ones, which are expressed in terms of a set of linear matrix inequalities (LMIs), to stabilize the StdNNs with MM switching exponentially.
Journal ArticleDOI
Stability of hybrid dynamic systems containing singularly perturbed random processes
G. Badowski,G.G. Yin +1 more
TL;DR: It is shown that if the limit dynamic systems and the perturbed Lyapunov methods are stable, then so are the original systems, which justifies the replacement of a complicated original system by its limit from a longtime behavior point of view.
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Stochastic stability of neutral-type Markovian-jumping BAM neural networks with time varying delays
TL;DR: A linear matrix inequality (LMI) approach is developed to establish sufficient conditions and novel delay-dependent conditions are established for the stochastic asymptotic stability of Markovian jumping BAM neural networks.
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Robust Finite-Time H ∞ Control for Nonlinear Jump Systems via Neural Networks
TL;DR: A neural network-based robust finite-time H∞ control design approach for a class of nonlinear Markov jump systems (MJSs) and results are given to illustrate the effectiveness of the developed theoretic results.
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.