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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Journal ArticleDOI
$H_{\infty}$ FEEDBACK CONTROLS BASED ON DISCRETE-TIME STATE OBSERVATIONS FOR SINGULAR HYBRID SYSTEMS WITH NONHOMOGENEOUS MARKOVIAN JUMP
Zhiyong Ye,Suying Pan,Jin Zhou +2 more
TL;DR: In this paper, a feedback controller based on discrete-time state observations, employing a stochastic Lyapunov-Krasovskii functional, and combining with the linear matrix inequalities (LMIs) technologies, sufficient conditions under the case of nonhomogeneous transition rates are developed such that the controlled system is regular, impulse free, and stochastically stable.
Proceedings ArticleDOI
Hybrid switching diffusions: Continuity and differentiability
Gang George Yin,Chao Zhu +1 more
TL;DR: This work focuses on hybrid switching diffusion systems and presents basic models for continuous and smooth dependence on initial data, whereas the verbatim proofs can be found in [35].
Journal ArticleDOI
A robust adaptive control design for a class of uncertain nonlinear markovian jump systems
TL;DR: In this paper, a Lyapunov-based adaptive nonlinear control scheme for a class of uncertain nonlinear Markovian jump systems with nonlinear state-dependent uncertainty is presented.
Proceedings ArticleDOI
Stability of Neutral Stochastic Dynamic Systems with Markovian Switching
TL;DR: Stability of neutral stochastic partial differential dynamic systems with Markovian switching is considered and some new sufficient conditions proving the stability in mean square of this neutral stoChastic dynamic systems are derived by employing the fixed point approach.
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.