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
p-th moment exponential stabilization of a class of stochastic hybrid systems via sampling data for the case p>2
Feng Lingyu,Zhang Jian,Mu Xiaowu +2 more
TL;DR: In this paper, the authors studied the exponential stability in the p-th moment for a class of stochastic hybrid systems by feedback control based on the discrete-time observations of system information, and also verified the corresponding almost sure exponential stability of the closed-loop system.
Journal ArticleDOI
Stability of two-time scale linear stochastic hybrid systems
Ewelina Seroka,Lesław Socha +1 more
TL;DR: In this paper, the problem of exponential mean-square stability of two-time scale, linear stochastic hybrid systems has been studied, and two basic approaches of stability analysis, for one-time hybrid systems with a Markovian switching rule as well as switching rule and singularly perturbed nonhybrid systems, were combined.
Journal ArticleDOI
Discrete-time control for highly nonlinear neutral stochastic delay systems
TL;DR: In this paper , the discrete-time state feedback control problem for neutral stochastic delay systems (NSDSs) in which coefficients satisfy highly nonlinear properties is explored, and a more general Lyapunov function is constructed to prove that the designed controller can stabilize the corresponding systems.
Journal ArticleDOI
On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays
Xinghua Liu,Hongsheng Xi +1 more
TL;DR: In this article, the exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated.
Posted Content
Stability of hybrid pantograph stochastic functional differential equations
Hao Wu,Junhao Hu,Chenggui Yuan +2 more
TL;DR: In this paper, a new type of stochastic functional differential equations, called hybrid pantograph SDFs, was introduced, and the authors investigated several moment properties and sample properties of the solutions to the equations by using the method of multiple Lyapunov functions, such as the moment exponential stability, almost sure exponential stability and almost sure polynomial stability.
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.