Periodic orbits from Δ-modulation of stable linear systems

The /Delta/-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by c/T/x where c /isin/R/n//bsol/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2004-08, Vol.49 (8), p.1376-1380
Main Authors: XIAOHUA XIA, ZINOBER, Alan S. I
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Computer science
control theory
systems
Control system analysis
Control systems
Control theory. Systems
Exact sciences and technology
Linear systems
Mathematical analysis
Modulation
Orbits
Polyhedrons
Vectors (mathematics)
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Summary:The /Delta/-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by c/T/x where c /isin/R/n//bsol/{0} is a given, otherwise arbitrary, vector. We obtain necessary and sufficient conditions for the existence of periodic points of a finite order. Some concrete results about the existence of a certain order of periodic points are also derived. We also study the relationship between certain polyhedra and the periodicity of the /Delta/-modulated orbit.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2004.832664