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
H ∞ analysis for a class of Markov jump nonlinear systems
TL;DR: A sufficient condition for disturbance attenuation in terms of linear matrix inequalities is developed which ensures robust stochastic mean square stability and uses a mode based Lyapunov function.
Journal ArticleDOI
Noise-to-state exponential stability of neutral random nonlinear systems
TL;DR: In this article, the existence and uniqueness of the solution to neutral random functional nonlinear systems (NRFSs) are established and the criteria on noise-to-state stability in the moment of a special class of NRFSs are derived.
Journal Article
The Strict Stability of Impulsive Stochastic Functional Differential Equations with Markovian Switching
TL;DR: Using Lyapunov functions and Razumikhin technique, the authors have obtained some criteria for the strict stability of impulsive stochastic functional differential equations with markovian switching.
Proceedings ArticleDOI
Observer-based finite-time control for discrete fuzzy jump nonlinear systems with time delays
TL;DR: Sufficient criteria on stochastic finite-time H∞ stabilization via observer-based fuzzy state feedback are provided for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities.
Journal ArticleDOI
L1 control for Itô stochastic nonlinear networked control systems
TL;DR: This paper investigates L1 control problem for a class of nonlinear stochastic networked control systems (NCSs) described by Takagi-Sugeno (T-S) fuzzy model by exploiting a delay-dependent and basis-dependent Lyapunov-Krasovskii function and by means of the Itô Stochastic differential equation technique, results on stability and L1 performance are proposed.
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.