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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Robust stability and stabilization of linear stochastic systems with Markovian switching and uncertain transition rates
TL;DR: In this paper, the robust stabilization problem for a class of linear uncertain stochastic systems with Markovian switching was studied, which involves parameter uncertainties both in the system matrices and in the mode transition rates matrix.
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Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations
TL;DR: In this article, state-feedback controls based on discrete-time observations are designed in the drift and diffusion parts of the system, which will be robustly exponentially stable in mean-square.
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A stochastic switched SIRS epidemic model with nonlinear incidence and vaccination: Stationary distribution and extinction
TL;DR: In this paper, a stochastic epidemic system with both switching noise and white noise is proposed to investigate the dynamics of the diseases and nonlinear incidence and vaccination strategies are also proposed.
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Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters
TL;DR: In this paper, the mean square exponential stabilization problem of stochastic bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time-varying delays is addressed.
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On pth moment exponential stability of stochastic differential equations with Markovian switching and time-varying delay
Enwen Zhu,Xue Tian,Yueheng Wang +2 more
TL;DR: In this article, the pth moment exponential stability of general nonlinear stochastic differential equations with Markovian switching and time-varying delay was investigated and sufficient conditions on pth moments exponential stability were derived by using the Lyapunov function and the generalized Halanay inequality.
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.