Representations and structural properties of periodic systems


Aleixo, José Carlos and Polderman, Jan Willem and Rocha, Paula (2007) Representations and structural properties of periodic systems. Automatica, 43 (11). pp. 1921-1931. ISSN 0005-1098

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Abstract:We consider periodic behavioral systems as introduced in [Kuijper, M., & Willems, J. C. (1997). A behavioral framework for periodically time-varying systems. In Proceedings of the 36th conference on decision & control (Vol. 3, pp. 2013–2016). San Diego, California, USA, 10–12 December 1997] and analyze two main issues: behavioral representation, and controllability/autonomy. More concretely, we study the equivalence and the minimality of kernel representations, and introduce latent variable (and, in particular, image) representations. Moreover we relate the controllability of a periodic system with the controllability of an associated time-invariant system known as lifted system, and derive a controllability test. Further, we prove the existence of an autonomous/controllable decomposition similar to the time-invariant case. Finally, we introduce a new concept of free variables and inputs, which can be regarded as a generalization of the one adopted for time-invariant systems, but appears to be more adequate for the periodic case.
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Copyright:© 2007 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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