Journal ArticleDOI
Stochastic stability properties of jump linear systems
TLDR
In this paper, the authors studied stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties, and showed that all second moment stability properties are equivalent and are sufficient for almost sure sample path stabilisation.Abstract:
Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented. Finally, for one-dimensional jump linear system, it is proved that the region for delta -moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0/sup +/. >read more
Citations
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Proceedings ArticleDOI
Stabilization of differential inclusion systems with Markovian jumping
Hongliang Liu,S. Ding,Huibo Zhou +2 more
TL;DR: In this paper, the stabilization of differential inclusions with Markovian jumping is discussed and the feedback control law is obtained to make the closed-loop system exponentially stable in the mean square.
Book ChapterDOI
Control and Filtering for Semi-Markovian Jump Systems Introduction
Fanbiao Li,Peng Shi,Ligang Wu +2 more
Journal ArticleDOI
Robust H∞ Control of Markov Jump Linear Systems with Uncertain Switching Probabilities
S M Hussin,V G Sufiyanov +1 more
TL;DR: In this article, the authors proposed a method to solve the problem of the lack of a sufficient number of translational data points for a given task by using the information from the user's profile.
Proceedings ArticleDOI
Stochastic robust stability analysis for discrete-time neural networks with Markovian jumping parameters and time delays
TL;DR: In this paper, the stochastic robust stability analysis for uncertain discrete-time delayed neural networks with Markovian jumping parameters is investigated based on linear matrix inequality (LMI) methodology.
Proceedings ArticleDOI
Robust Kalman filtering for continuous-time Markovian jump uncertain systems
TL;DR: In this article, the problem of Kalman filtering for a class of uncertain linear continuous-time systems with Markovian jumping parameters is studied, and the system under consideration is subjected to time-varying norm-bounded parameter uncertainties in the state and measurement equations.
References
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Book
Stochastic Stability and Control
TL;DR: In this article, a book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes is presented, which is based on the work of this article.
Journal ArticleDOI
Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control
Y. Ji,Howard J. Chizeck +1 more
TL;DR: In this paper, necessary and sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite-time Markovian jump linear quadratic (JLQ) problem are established.
Random differential equations in control theory
TL;DR: In this article, the authors discuss control processes and optimization problems solutions by stochastic differential equations, discussing dynamic models and programming, linear filtering and optimal feedback, and discuss linear filtering with optimal feedback.
Journal ArticleDOI
A survey of stability of stochastic systems
TL;DR: The main purpose of this manuscript is to give some understanding of the subject of stability of stochastic systems by presenting some of the basic ideas as well as a survey of results that have appeared in the literature.
Journal ArticleDOI
Feedback control of a class of linear systems with jump parameters
TL;DR: In this paper, a class of linear systems are studied which are subject to sudden changes in parameter values and an algorithm similar in form to Kushner's stochastic maximum principle is derived.