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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Stabilization and destabilization of nonlinear systems via intermittent stochastic noise with application to memristor-based system
TL;DR: Some distinct conditions and conclusions on almost sure exponential stability and instability, which are related to the control period T and the noise width δ are given and exploited to examine stabilization and destabilization via intermittent stochastic perturbation and applied to the stabilization of a memristor-based chaotic system.
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Stability analysis of stochastic differential equations with Markovian switching
TL;DR: By using the switching process jump times to subdivide the “time” and then investigate the related sequence, sufficient conditions for asymptotic stability of SDEWMSs are provided when each subsystem is stable and a certain “slow switching” condition holds.
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Adaptive sliding mode controller design of Markov jump systems with time-varying actuator faults and partly unknown transition probabilities
TL;DR: By Lyapunov stability theory, some sufficient conditions of stochastic stability for Markov jump systems in the existence of actuators faults, unknown nonlinearities and unknown perturbation are derived.
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Delay-dependent stability and stabilizability of uncertain jump bilinear stochastic systems with mode-dependent time-delays
TL;DR: Novel delay-dependent sufficient conditions in terms of linear matrix inequalities are derived for robust stability and robust stabilizability for a class of uncertain jump bilinear stochastic systems with mode-dependent time delays.
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Numerical Solutions for Stochastic Differential Games With Regime Switching
TL;DR: Numerical methods using Markov chain approximation techniques are developed and a new proof of the existence of a saddle point for the stochastic differential game is provided, enabling us to treat certain systems with nonseparable structure.
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.