Representations and structural properties of periodic systems

José Carlos Aleixo, Jan W. Polderman, Paula Rocha

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    12 Citations (Scopus)


    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.
    Original languageUndefined
    Article number10.1016/j.automatica.2007.03.013
    Pages (from-to)1921-1931
    Number of pages11
    Issue numberLNCS4549/11
    Publication statusPublished - Nov 2007


    • MSC-93C05
    • EWI-11269
    • METIS-242206
    • MSC-93C55
    • IR-61970

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