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Periodic orbits from Δ-modulation of stable linear systems

By X. Xia and A. Zinober


The �-modulated control of a single input, discrete time, linear stable system is investigated. The modulation direction is given by cTx where c �Rn/{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 �-modulated orbit.\ud \u

Publisher: Institute of Electrical and Electronics Engineers
Year: 2004
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