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  • 1
    Electronic Resource
    Electronic Resource
    Homogeneous behaviors (1997)
    Springer
    Mathematics of control, signals, and systems 10 (1997), S. 61-75 
    Details
    ISSN: 1435-568X
    Keywords: Linear behavior ; Compactification of systems ; Shift spaces ; Grothendieck quotient scheme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract Recently a smooth compactification of the space of linear systems withn states,m inputs, andp outputs has been discovered. In this paper we obtain a concrete interpretation of this compactification as a space of discrete-time behaviors. We use both homogeneous polynomial representations and generalized firstorder representations, and provide a realization theory to link these to each other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01219776
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  • 2
    Electronic Resource
    Electronic Resource
    A Behavioral Approach to Singular Systems (1998)
    Springer
    Acta applicandae mathematicae 54 (1998), S. 331-344 
    Details
    ISSN: 1572-9036
    Keywords: behaviors ; singular systems ; shift spaces ; coherent sheaves
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The notion of behaviors introduced by Willems gives a good description of dynamicalsystems without reference to any particular representation of the system in terms of equations. Inthis note, we introduce a notion of behaviors that allows us to describe singular systems in a verynatural way. The new definition of behaviors given here is closely related to that of a sheaf overthe projective line, and we make this connection precise.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006106222280
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  • 3
    Electronic Resource
    Electronic Resource
    A smooth compactification of the space of transfer functions with fixed McMillan degree (1994)
    Springer
    Acta applicandae mathematicae 34 (1994), S. 329-352 
    Details
    ISSN: 1572-9036
    Keywords: 93B25 ; 93C35 ; 32J05 ; 14M15 ; Transfer functions ; compactification ; Quot scheme ; Hermann-Martin curve
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is a classical result of Clark that the space of all proper or strictly properp ×m transfer functions of a fixed McMillan degreed has, in a natural way, the structure of a noncompact, smooth manifold. There is a natural embedding of this space into the set of allp × (m+p) autoregressive systems of degree at mostd. Extending the topology in a natural way we will show that this enlarged topological space is compact. Finally we describe a homogenization process which produces a smooth compactification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00998684
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