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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Finite-Time Gain-Scheduled Control on Stochastic Bioreactor Systems with Partially Known Transition Jump Rates
TL;DR: An observer-based finite-time continuous gain-scheduled control is designed for a class of stochastic bioreactor systems with partially known jump rates to ensure robust finite- time stabilization of the each jump linear system by means of linear matrix inequalities.
Journal ArticleDOI
On exponential stability of neutral delay Markovian jump systems with nonlinear perturbations and partially unknown transition rates
Xinghua Liu,Hongsheng Xi +1 more
TL;DR: In this article, the exponential stability for neutral delay Markovian jump systems with nonlinear perturbations and partially unknown transition rates is investigated with creative Lyapunov functional and novel matrix inequalities analysis, and the delay-range-dependent and rate-dependent exponential stability conditions are presented by reciprocally convex lemma and free weighting matrices.
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Razumikhin-type theorems of neutral stochastic functional differential equations
Zhou Shao-bo,Hu Shigeng +1 more
TL;DR: In this article, the stability of stochastic functional differential equations with Markovian switching was studied and a Razumikhin-type theorem was established for the neutral stochastically functional differential equation without Markovians.
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Stabilization of Hybrid Systems by Feedback Control Based on Discrete‐Time State and Mode Observations
TL;DR: In this paper, a feedback control based on discrete-time state observations was proposed to stabilize continuous-time hybrid stochastic systems in the mean-square sense, where the mode is identified at discrete times when the state is observed.
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Non-fragile robust stabilization and H ∞ control for uncertain stochastic time delay systems with Markovian jump parameters and nonlinear disturbances
TL;DR: In this paper, the authors considered the problem of non-fragile robust stabilization and control for uncertain stochastic time delay systems with Markovian jump parameters and nonlinear disturbances.
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.