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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The Linear Quadratic Optimization Problems for a Class of Linear Stochastic Systems With Multiplicative White Noise and
Vasile Dragan,Toader Morozan +1 more
TL;DR: The linear quadratic optimization problem for a class of linear stochastic systems subject both to multiplicative white noise and Markovian jumping is investigated and an iterative procedure to compute the maximal solution of the systems of generalized Riccati equations is provided.
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Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks With Time-Varying Delays
Xuyang Lou,Baotong Cui +1 more
TL;DR: This correspondence provides stochastic exponential stability for Markovian jumping bidirectional associative memory neural networks with time-varying delays with an approach combining the Lyapunov functional with linear matrix inequality.
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A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates
TL;DR: In this article, a sliding mode control law is developed to drive the state trajectory of the closed-loop system to the specified linear switching surface in a finite-time interval in spite of the existing uncertainties, time delays and unknown transition rates.
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Gain-Scheduled Robust Fault Detection on Time-Delay Stochastic Nonlinear Systems
Yanyan Yin,Peng Shi,Fei Liu +2 more
TL;DR: In this paper, a continuous gain-scheduled approach is employed to design continuous RFDFs on the entire nonlinear jump system, and a sufficient condition on the existence of RFDF is established in terms of linear matrix inequality techniques.
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Robust peak-to-peak filtering for Markov jump systems
Shuping He,Fei Liu +1 more
TL;DR: The peak-to-peak filtering problem is studied for a class of Markov jump systems with uncertain parameters and the dynamic filtering error system is obtained by re-constructing the system and using appropriate stochastic Lyapunov-Krasovskii functional.
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.