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
Stabilizing Randomly Switched Systems
TL;DR: Stability analysis and stabilization of randomly switched systems under a class of switching signals modeled as a jump stochastic process independent of the system state are concerned.
Journal ArticleDOI
Event-triggered sliding mode control of networked control systems with Markovian jump parameters
TL;DR: In this article, a sliding mode control for networked Markovian jump systems with partially-known transition probabilities via an event-triggered scheme was proposed to reduce network bandwidth usage and save network resources.
Journal ArticleDOI
H 2 state feedback controller design for continuous Markov jump linear systems with partly known information
Mouquan Shen,Guang-Hong Yang +1 more
TL;DR: By decoupling the unknown transition probabilities from the Lyapunov matrices, new sufficient conditions for the H 2 performance analysis of the considered systems are derived in terms of linear matrix inequalities (LMIs).
Journal ArticleDOI
Generalized joint spectral radius and stability of switching systems
Masaki Ogura,Clyde F. Martin +1 more
TL;DR: In this paper, the generalized joint spectral radius with exponents (GJSR) was extended to probability distributions, and the authors investigated the mean stability of switching systems, and established the equivalence of mean square stability, simultaneous contractibility in square mean and the existence of a quadratic Lyapunov function.
Journal ArticleDOI
Robust fault detection of Markovian jump systems
TL;DR: In this article, an observer-based robust fault detection for both continuous and discrete-time linear Markovian jump systems with an unknown input is considered. But the robustness of the observer is not considered.
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.