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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Brief paper: A unified design for state and output feedback H∞ control of nonlinear stochastic Markovian jump systems with state and disturbance-dependent noise
TL;DR: A unified design is given for both state and dynamic output feedback H"~ control via a common function u(@?, r"t) (i.e., u(x,r"t), which is a state feedback H%"~ control, while u([email protected]?,r" t) is the desired output Feedback H" ~ control).
Journal ArticleDOI
Consensus Over Numerosity-Constrained Random Networks
Nicole Abaid,Maurizio Porfiri +1 more
TL;DR: This network construction models the perceptual phenomenon of numerosity observed in animal groups exhibiting collective behavior and derives a closed form expression for the asymptotic convergence factor.
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On the detectability and observability of discrete-time Markov jump linear systems☆
TL;DR: A new detectability concept for discrete-time Markov jump linear systems with finite Markov state is presented, which generalizes the MS-detectability concept found in the literature and introduces a related observability concept that also generalizes previous concepts.
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Dwell time analysis of deterministic and stochastic switched systems
TL;DR: Being the minimum dwell time very hardly computable, viable procedures are proposed for a computation of an upper bound through Kronecker calculus, standard H∞ theory and coupled Lyapunov inequalities.
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.
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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.
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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.