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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Book ChapterDOI
Finite-Time Stability and Stabilization for Switching Markovian Jump Systems
TL;DR: In this paper , the authors extended the results of finite-time controller design to discrete-time switching Markovian jump systems with time-delay, and derived the relationship among three kinds of time scales, such as time delay, average dwell time and finite time interval, by means of the average dwell-time constraint condition.
Proceedings ArticleDOI
Lyapunov coupled equations for infinite jump linear systems
Marcelo D. Fragoso,J. Baczynski +1 more
TL;DR: In this article, it was shown that the Markov jump linear system (MJLS) is stochastically stabilizable (SS) if and only if the associated countably infinite coupled Lyapunov equations have a unique norm bounded strictly positive solution.
DissertationDOI
Distributed averaging over communication networks: Fragility, robustness and opportunities
TL;DR: The fragility of a popular distributed averaging algorithm when the information exchange among the nodes is limited by communication delays, fading connections and additive noise is studied and a novel mechanism of network feedback to mitigate effects of communication uncertainties on information aggregation is developed.
Proceedings ArticleDOI
Stability of random linear equations with applications
TL;DR: Some theoretical results established in the past few years on time-varying random linear equations with some refinements and extensions, which have direct applications in adaptive estimation are presented.
Journal ArticleDOI
Transition rate bounds for the stability robustness of continuous-time markovian jump linear systems
TL;DR: In this article, the stability robustness of Markovian jump linear systems in continuous-time with respect to their transition rates was investigated and a sufficient condition for the robust stochastic stability of the underlying system, which is in terms of an upper bound of the perturbed transition rate was developed.
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.