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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Almost Sure Exponential Stabilization of a Class of Uncertain Stochastic Systems with Markovian Switching
Proceedings ArticleDOI
Consensus Analysis for Multi-agent Systems with Markov Switching Hierarchical Network Topology
TL;DR: In this paper , the state consensus problem of multi-agent systems with Markov switching hierarchical network topology and inter-layer communication delay is studied, and the sufficient conditions of hierarchical consensus in form of linear matrix inequalities are derived.
Journal Article
Detectability Of Markov Jump Linear Systems, The Lq Problem And The Coupled Riccati Equations
Do Val J.B.R.,Eduardo F. Costa +1 more
TL;DR: In this paper, different detectability conditions that appear in the literature of Markov jump linear systems are collected and compared, and the role that those conditions play in the associated jump linear quadratic problem is clarified, as they appear as necessary and sufficient conditions for stability and positivity of solutions.
Proceedings ArticleDOI
Reduced order H ∞ filtering for discrete-time Markovian jump linear systems with partly known transition probabilities
Hong-Li Zhang,Xiao-Heng Chang +1 more
TL;DR: In this paper, the problem of H ∞ filtering for discrete Markov jump linear systems with partly known transition probability is investigated and an improved condition which can lead to potential less conservative result is obtained.
Book ChapterDOI
Observer-Based H∞ Output Feedback Control for Switched Systems with Sojourn Probability Method
TL;DR: The purpose of the addressed problem is to design the observer-based output feedback controller and to obtain sufficient conditions for the mean square stability of the system.
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.