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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Comments on “Finite-Time $H_{\infty }$ Fuzzy Control of Nonlinear Jump Systems With Time Delays Via Dynamic Observer-Based State Feedback”
TL;DR: In this paper, a defect appeared in finite-time H∞ fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback, which the observerbased H ∞ controller cannot ensure stochastic finite time boundedness, and satisfying a prescribed level of disturbance attenuation for the resulting closed-loop error fuzzy Markov jump systems.
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Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching
Zhao Jing Wu,Jun Yang,Peng Shi +2 more
TL;DR: An Ito formula is proposed for stochastic integral equations with an integral about martingale measure and an adaptive backstepping controller is designed such that the closed-loop system has a unique solution that is globally bounded in probability and L4-norm of the tracking error converges to an arbitrarily small neighborhood of zero.
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Technical communique: Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control
TL;DR: The aim here is to initiate the study in this area by establishing some new results in the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback controls.
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Stochastic stability of Ito differential equations with semi-Markovian jump parameters
TL;DR: The problem of stochastic stability for linear systems with jump parameters being semi-Markovianrather than full Markovian is further investigated and Ito type nonlinear Stochastic differential equations with phase type semi-markovian jump parameters are described.
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Stability of Stochastic Nonlinear Systems With State-Dependent Switching
TL;DR: The results presented depend on some easily-verified assumptions that are as elegant as those in the deterministic case, and the proofs themselves provide design procedures for switching controls.
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.