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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Control for Discrete-Time Stochastic Systems With Markovian Jumps and Multiplicative Noise
Ting Hou,Weihai Zhang,Hongji Ma +2 more
Journal Article
A new approach to robust finite-time H∞ control of continuous-time Markov jump systems
Proceedings ArticleDOI
A Note on Convergence in Maximal Solution Problems for Infinite Markov Jump Linear Systems
TL;DR: In this article, a condition for the spectrum of the limit of a bounded linear operator being in the closed left half-plane of the complex numbers of the Markov chain is presented.
Proceedings ArticleDOI
Robust stabilization and optimization of fault tolerant linear systems
TL;DR: Under the assumption of the existence of a suitable control law, the necessary and sufficient conditions for the stochastic stabilizability of the nominal model of this class of systems and optimality of the control law are given.
Journal ArticleDOI
Decay rates for stabilization of linear continuous-time systems with random switching
Fritz Colonius,Guilherme Mazanti +1 more
TL;DR: For a class of linear switched systems in continuous time, a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates as mentioned in this paper, based on the Multiplicative Ergodic Theorem applied to an associated system in discrete time.
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.