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
Finite-time stabilization for positive Markovian jumping neural networks
Chengcheng Ren,Shuping He +1 more
TL;DR: A suitable finite-time stabilizable controller is devised to guarantee the positiveness of the closed-loop MJNNs and some sufficient conditions for the existence of the controller gain solutions are proposed and proved by using the stochastic Lyapunov-Krasovskii functional approach and linear matrix inequalities techniques.
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p-Moment stability of stochastic differential equations with jumps
TL;DR: Several theorems on p-moment stability of stochastic differential equations with jumps are established using Liapunov function and an example is present to show application of the obtained results.
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Technical Communique: LMI-based robust H∞ control of uncertain linear jump systems with time-delays
TL;DR: This paper examines the robust mean square stabilization and robust H^~ control problem for a class of linear systems and a systematic approach via linear matrix inequalities (LMI) is proposed to solve the problem of concern.
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Stabilization of Markovian Systems via Probability Rate Synthesis and Output Feedback
Jun-e Feng,James Lam,Zhan Shu +2 more
TL;DR: A novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of Markovian jump linear systems.
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Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays
TL;DR: This paper considers the problems of delay-dependent robust stabilization and H∞ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays based on the Lyapunov method and introduces some appropriate free-weighting matrices.
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.