Abstract
In the previous chapter we saw examples of P representations that contain more internal variables than needed to represent the behavior of a system. As a matter of fact, we might distinguish between “small” and “large” P representations. In the first section of this chapter we consider the question: what do small P representations look like? Formulated differently, we ask ourselves: which parts of the pencil equations are essential for the representation of the behavior? We will specify what we call “minimal” P representations and characterize minimality in terms of the constant pencil matrices. The same issue will be investigated for D representations, DZ representations and DP representations in subsequent sections. We will give results under both strong and weak external equivalence. A new feature of the approach in these sections is that invariant lower bounds are derived for all items that are to be minimized.
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© 1994 Springer Science+Business Media New York
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Kuijper, M. (1994). Minimality and transformation groups. In: First-order Representations of Linear Systems. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0259-2_4
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DOI: https://doi.org/10.1007/978-1-4612-0259-2_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6684-6
Online ISBN: 978-1-4612-0259-2
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