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 Article
Mode-independent H ∞ filters for hybrid Markov linear systems
TL;DR: In this article, a method for designing an asymptotically stable linear time-invariant H∞ filter for continuous-time linear systems with Markovian jumping parameters is presented.
Posted Content
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
Shaikshavali Chitraganti,Samir Aberkane,Christophe Aubrun,Guillermo Valencia-Palomo,Vasile Dragan +4 more
TL;DR: In this article, a deterministic receding horizon control of discrete-time state-dependent jump linear systems with probabilistic state constraints is studied. But the authors focus on the stochastic switching system and do not consider the deterministic horizon control problem.
Journal ArticleDOI
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
Shaikshavali Chitraganti,Samir Aberkane,Christophe Aubrun,Guillermo Valencia-Palomo,Vasile Dragan +4 more
TL;DR: In this article, a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, is considered, subject to possibly unbounded random disturbances and probabilistic state constraints, and converted to deterministic constraints using inverse cumulative distribution function.
Journal ArticleDOI
On Robust stability of singular systems with random abrupt changes
TL;DR: In this article, sufficient conditions on stochastic stability and robust stability for the class of continuous-time singular linear systems with Markovian switching have been developed in the LMI setting, and the developed sufficient conditions are used to check if either the nominal or the uncertain systems are regular, impulse-free, and stochastically stable or robust.
Journal ArticleDOI
Robust Control for Linear Systems with Markovian Jumping Parameters
TL;DR: In this paper, the problem of robust control for linear systems with Markovian jumping parameters and parametric uncertainty is investigated, and a methodology is proposed for the design of robust state feedback controllers.
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.