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
Successful couplings for diffusion processes with state-dependent switching
Fubao Xi,Jinghai Shao +1 more
TL;DR: In this article, successful couplings for a class of multidimensional diffusion processes with state-dependent switching are investigated. And sufficient conditions to guarantee this type of couplings to be successful are provided.
Proceedings ArticleDOI
Robust delay-feedback control for discrete-time stochastic interval systems with time-delay and Markovian jumps
Guici Chen,Yu Gao,Shasha Zhu +2 more
TL;DR: The robust delay feedback control problems for discrete-time stochastic interval systems(DTSISs) with time-delay and Markovian jumps are studied and a robust delay-feedback controller is designed.
Journal ArticleDOI
Implicit numerical methods for neutral stochastic differential equations with unbounded delay and Markovian switching
TL;DR: It is proved that the discrete backward Euler equilibrium solution is globally a.s. asymptotically exponentially stable without the linear growth condition on the drift coefficient.
Journal ArticleDOI
Stabilization for a class of stochastic nonlinear systems with arbitrary switching via the common Lyapunov function method
TL;DR: Based on the simultaneous domination approach, the common Lyapunov function method and the backstepping technique, a state feedback controller and an output feedback controller are designed, respectively.
Posted Content
A mesoscopic approach on stability and phase transition between different traffic flow states
TL;DR: In this article, the authors explore the underlying physics of the traffic system, by examining closely the physical properties and mathematical constraints of the phase transitions therein, and reveal its close connections to the instability of the equation of motion and to the transition between different traffic states.
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.