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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Proceedings ArticleDOI
Stabilization on fuzzy Markovian jump systems with uncertain switching probabilities
TL;DR: In this paper, the robust control problem for fuzzy Markovian time-delay jump systems with uncertain switching probabilities is considered. But the transition rate matrix of the Markov process and the parameters of the system are uncertain but belong to a given polytope.
Journal ArticleDOI
Stabilization of hybrid stochastic systems with time-varying delay by discrete-time state feedback control
TL;DR: In this article , the authors show that hybrid stochastic systems with variable delay can be stabilized by discrete-time state feedback control as long as Θ(τ + τ + τ * ) ≥ 0, where τ is the duration τ between two consecutive state observations.
Proceedings ArticleDOI
Interval stabilization of stochastic Markov jump systems
Meijun Zhu,Li Sheng,Yuhong Wang +2 more
TL;DR: In this article, a sufficient condition for the interval stabilization problem of stochastic Markov jump systems in terms of linear matrix inequalities is proposed, and a numerical example is presented to illustrate the effectiveness of the obtained results.
Further results on delay-dependent exponential stability for uncertain stochastic neural networks with mixed delays and Markovian jump parameters
TL;DR: In this article, the robustly exponential stability of uncertain stochastic neural nets with mixed delays and Markovian jump parameters was studied. And the derived results shown by three illustrative examples are more effective than some existing ones.
Journal ArticleDOI
Stability of a Class of Stochastic Nonlinear Systems with Markovian Switching
Xiaohua Liu,Wuquan Li +1 more
TL;DR: This paper investigates the stability of a class of stochastic nonlinear systems with Markovian switching via output-feedback using the backstepping design method and homogeneous domination technique to guarantee that the closed-loop system has a unique solution and is almost surely asymptotically stable.
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.
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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.