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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Journal ArticleDOI
Stability of discrete-time linear systems with Markovian jumping parameters and constrained control
TL;DR: The approach of positively invariant sets is used to obtain new necessary and sufficient conditions for positive invariance, and enough conditions for stochastic stability for linear discrete-time systems with Markovian jumping parameters and constrained control.
Journal ArticleDOI
Distributed Averaging Under Constraints on Information Exchange: Emergence of Lévy Flights
Jing Wang,Nicola Elia +1 more
TL;DR: This work is the first, to the best of the knowledge, to establish the intimate relationship between the propagation of channel uncertainties in networked systems, the MS stability robustness and the emergence of Lévy flights in distributed averaging systems.
Stability analysis of linear control systems with uncertain parameters
TL;DR: Fang et al. as discussed by the authors investigated the properties of various types of moment stability for stochastic jump linear systems, and used large deviation theory to study the relationship between lower moment stability and almost sure stability.
Robust Filtering for Uncertain Markovian Jump Systems With Mode-Dependent Time Delays
TL;DR: The aim of this problem is to design a Markovian jump linear filter that ensures robust exponential mean-square stability of the filtering error system and a prescribed L/sub 2/- induced gain from the noise signals to the estimation error, for all admissible uncertainties.
Journal ArticleDOI
Stochastic stability and robust control for sampled-data systems with Markovian jump parameters
Li-Sheng Hu,Peng Shi,Biao Huang +2 more
TL;DR: In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied, and sufficient conditions for the existence of a sampled data feedback control and a multirate sampled data optimal control for the continuous-time uncertain Markovian jump systems are obtained.
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.