Periodic Behaviors

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2010Embargo end date: 01 Jan 2010 Netherlands English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Control and Optimization, volume 48, pages 4,652-4,663 (issn: 0363-0129, eissn: 1095-7138,

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Authors: Diego Napp Avelli; Marius van der Put; Shiva Shankar;

doi: 10.1137/100782577 , 10.48550/arxiv.1001.2255

arXiv: 1001.2255

handle: 11370/4b5ea5b2-2230-4193-9629-25de204ae9ea

Periodic Behaviors

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Abstract

This paper studies behaviors that are defined on a torus, or equivalently, behaviors defined in spaces of periodic functions, and establishes their basic properties analogous to classical results of Malgrange, Palamodov, Oberst et al. for behaviors on R^n. These properties - in particular the Nullstellensatz describing the Willems closure - are closely related to integral and rational points on affine algebraic varieties.

13 pages

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Netherlands

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Keywords

STABILIZATION, periodic behaviors, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), SYSTEMS, Optimization and Control (math.OC), 93C05, 93C35, 93B25, 93C20, 35B10, 35E20, FOS: Mathematics, Mathematics - Optimization and Control, Willems' closure, behaviors on torii, injective hull

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