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
Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters
TL;DR: In this paper, the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters were investigated, and sufficient conditions were derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered GA networks.
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Output Tracking of Stochastic High-Order Nonlinear Systems with Markovian Switching
Wuquan Li,Zhaojing Wu +1 more
TL;DR: This technical note poses and solves the output tracking problem for a class of stochastic high-order nonlinear systems with stationary Markovian switching by introducing a II-operator and using Dynkin formula for Markovia switching systems.
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Fault Tolerant Formations Control of UAVs Subject to Permanent and Intermittent Faults
TL;DR: A fault tolerant control (FTC) scheme is developed to accommodate the permanent fault and it is shown that for the intermittent fault, the formation stability can be maintained under some conditions of fault appearance and disappearance without requiring to take any FTC action.
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Fuzzy model‐based fault detection for Markov jump systems
Shuping He,Fei Liu +1 more
TL;DR: In this paper, the robust fault detection filter (RFDF) design problems for nonlinear stochastic time-delay Markov jump systems were studied by means of the Takagi-Sugeno fuzzy models, the fuzzy RFDF system and the dynamics of filtering error generator were constructed.
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Stability of stochastic neural networks of neutral type with Markovian jumping parameters: A delay-fractioning approach ☆
TL;DR: The obtained results are shown to be much less conservative via constructing a new Lyapunov–Krasovskii functional and the idea of “delay fractioning”, which can be easily facilitated by using the standard numerical software.
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.