Abstract
This tutorial and expository paper considers linear dynamical systems ẋ = Fx + Gu, y = Hx, or, x(t+1) = Fx(t) + Gu(t), y(t) = Hx(t); more precisely it is really concerned with families of such, i.e., roughly speaking, with systems like the above where now the matrices F,G,H depend on some extra parameters a. After discussing some motivation for studying families (delay systems, systems over rings, n-d systems, perturbed systems, identification, parameter uncertainty) we discuss the classifying of families (fine moduli spaces). This is followed by two straightforward applications: realization with parameters and the nonexistence of global continuous canonical forms. More applications, especially to feedback will be discussed in Chris Byrnes’ talks at this conference and similar problems as in these talks for networks will be discussed by Tyrone Duncan. The classifying fine moduli space cannot readily be extended and the concluding sections are devoted to this observation and a few more related results.
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Hazewinkel, M. (1980). (Fine) Moduli (Spaces) for Linear Systems: What are they and what are they Good for?. In: Byrnes, C.I., Martin, C.F. (eds) Geometrical Methods for the Theory of Linear Systems. Nato Advanced Study Institutes Series, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9082-1_3
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DOI: https://doi.org/10.1007/978-94-009-9082-1_3
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