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
More filters
Journal Article
New stability criteria for a class of markovian jumping genetic regulatory networks with time-varying delays
TL;DR: New stability criteria are proposed in terms of linear matrix inequalities, which can guarantee the mean square stability of Markovian jumping GRNs, by constructing a novel Lyapunov-Krasovskii functional and using an appropriate enlargement scheme.
Journal ArticleDOI
Stabilisation of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay
TL;DR: In this paper, the mean-square exponential stability of the controlled system is investigated and the time delay is taken into account for the discrete-time state observation in a continuous research to Mao (2013).
Journal ArticleDOI
Almost Sure Stabilization for Feedback Controls of Regime-Switching Linear Systems With a Hidden Markov Chain
TL;DR: Under simple conditions, it is shown that as long as the feedback controls have linear growth in the continuous component, the resulting process is regular and by appropriate choice of the Lyapunov functions, it was shown that the adaptive system is stabilizable almost surely.
Journal ArticleDOI
Robust finite-time H∞ control for uncertain discrete jump systems with time delay
TL;DR: This paper addresses the robust finite-time H ∞ control problem for a family of uncertain discrete-time Markovian jump systems with time delay using Lyapunov approach and simulating examples are presented to demonstrate the validity of the developed techniques.
Journal ArticleDOI
Optimal finite-time passive controller design for uncertain nonlinear Markovian jumping systems
Shuping He,Fei Liu +1 more
TL;DR: The Takagi and Sugeno (T–S) fuzzy model is employed to represent the nonlinear system with Markovian jump parameters and norm-bounded uncertainties and gives a sufficient condition for the existence of finite-time passive controller such that the uncertain nonlinear MJSs is stochastically finite- time bounded for all admissible uncertainties.
References
More filters
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.