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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On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters
TL;DR: This work focuses on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay.
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Stability analysis for stochastic hybrid systems
TL;DR: This survey addresses stability analysis for stochastic hybrid systems (SHS) by reviewing many of the stability concepts that have been studied, including Lyapunov stability, Lagrange stability, asymptotic stability, and recurrence.
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Brief paper: Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching
TL;DR: A more general class of stochastic nonlinear systems with Markovian switching with stable stability criteria and the existence theorem of strong solution are considered.
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Brief paper: Sliding mode control for Itô stochastic systems with Markovian switching
TL;DR: In this paper, a sliding mode controller including the transition rates of modes can cope with the effect of Markovian switching by means of linear matrix inequalities with equality constraint, sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with @c-disturbance attenuation level.
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Stabilization and destabilization of hybrid systems of stochastic differential equations
TL;DR: New methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided, and these results are used to examine stochastically stabilization and destabilization.
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.