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Output digitization of simple measure-preserving linear systems

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We examine three simple linear systems from the viewpoint of ergodic theory.We digitize the output and record only the sign of the output at integer times.We show that even with this minimal output we can recover important information about the systems.In particular,for a two-dimensional system viewed as a flow on the circle,we can determine the rate of rota-tion.We then use these results to determine the slope of the trajectories for constant irrational flow on the two-dimensional torus.To achieve this,we randomize the system by partitioning the state space and only recording which partition the state is in at each integer time.We show directly that these systems have entropy zero.Finally,we examine two four-dimensional systems and reduce them to the study of linear flows on the two-dimensional torus.

ErgodicLinear systemObservabilityCantor set

A.DeStefano、M.Thitsa、C.Martin

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Department of Mathematics and Computer Science,College of the Holy Cross,Worcester,MA 01610,USA

Department of Electrical and Computer Engineering,Mercer University,Macon,GA 31207,USA

Department of Mathematics and Statistics,Texas Tech University,Lubbock,TX 79430,USA

2021

控制理论与技术(英文版)
华南理工大学

控制理论与技术(英文版)

CSCDEI
影响因子：0.307
ISSN：2095-6983
年,卷(期)：2021.19(4)
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