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
Robust finite-time stabilization of uncertain singular Markovian jump systems
TL;DR: In this paper, the authors studied the problem of robust finite-time stabilization for one family of uncertain singular Markovian jump systems with parametric uncertainties and time-varying norm-bounded disturbance.
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Threshold dynamics and ergodicity of an SIRS epidemic model with Markovian switching
Dan Li,Shengqiang Liu,Jingan Cui +2 more
TL;DR: In this article, the authors studied the threshold dynamics and ergodicity of a stochastic SIRS epidemic model with the disease transmission rate driven by a semi-Markov process.
Journal ArticleDOI
Nonlinear filtering for state delayed systems with Markovian switching
TL;DR: The purpose of the problem addressed is to design a nonlinear full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially stable in the mean square.
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Networked Control With Reset Quantized State Based on Bernoulli Processing
Renquan Lu,Fang Wu,Anke Xue +2 more
TL;DR: By the stochastic Lyapunov method, it is derived that the error system under the proposed reset technique is asymptotically stable in the sense of each discrete “reset” time instant, and mean-squarestable in the continuous-time domain except those ‘reset’ time instants.
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Razumikhin method and exponential stability of hybrid stochastic delay interval systems
TL;DR: In this paper, the Razumikhin method is developed to cope with the difficulty arising from the non-differentiability of the time delay in hybrid stochastic delay interval systems with Markovian switching.
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.