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
On Stability and Stabilizability of Singular Stochastic Systems with Delays
TL;DR: In this article, a design algorithm for a state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse free, and stochastically stable is proposed in terms of the solutions to linear matrix inequalities.
Journal ArticleDOI
p th moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay
Quanxin Zhu,Qiuyan Zhang +1 more
TL;DR: In this article, the authors considered the stability of hybrid stochastic differential equations by feedback control based on discrete-time state observations and established an upper bound on the duration τ between two consecutive state observations.
Journal ArticleDOI
H∞ consensus for nonlinear stochastic multi-agent systems with time delay
TL;DR: Both delay-independent and delay-dependent stochastic bounded real lemmas are developed and sufficient conditions on the existence of the desired dynamic output feedback protocol are presented in the form of linear matrix inequalities.
Proceedings ArticleDOI
Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching
Zhaojing Wu,Xuejun Xie +1 more
TL;DR: In this article, a more general class of stochastic nonlinear systems with Markovian switching is considered, and the stability criteria and the existence theorem of strong solution are firstly presented by using the inequality of mathematic expectation of Lyapunov function and its infinitesimal generator.
Journal ArticleDOI
Robust finite-time H∞ control for Markovian jump systems with partially known transition probabilities
TL;DR: Sufficient conditions ensuring the finite-time boundedness, H ∞ finite- time boundedness and finite- Time-Finite-time state feedback stabilization are developed for the given system for the first time.
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.