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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Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain
TL;DR: In this paper, the authors focus on the almost sure stabilization of adaptive control systems that involve an unknown Markov chain and show that the adaptive system is stabilizable almost surely under simple conditions.
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Finite-Time $$L_1$$L1 Control for Positive Markovian Jump Systems with Partly Known Transition Rates
TL;DR: A key point of this paper is to extend the special requirement of completely known transition rates to more general form that covers completely known and completely unknown transition rates as two special cases.
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Stability of Impulsive Stochastic Delay Systems with Markovian Switched Delay Effects
TL;DR: In this paper , the pth moment exponential stability of impulsive stochastic delay systems with Markovian switched delay effects was investigated, where the delay is a Markov chain.
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Synchronisation control for neutral-type multi-slave stochastic hybrid systems
TL;DR: An exponential synchronisation problem for neutral-type multi-slave hybrid systems with stochastic perturbation is discussed, where the adaptive synchronisation model involves a master system and multiple slave systems and a sufficient condition is obtained to guarantee the stability of the error system.
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Input-to-state stability of hybrid stochastic systems with unbounded delays and impulsive effects
TL;DR: The results show that the ISS properties still remain under certain impulsive perturbations for some continuous stable systems, and indicate that an unstable system can be successfully stabilized to be input-to-state stable by impulses even if the corresponding continuous system is unstable.
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.