Controllability and differential flatness of linear analytic ordinary differential systems
(dedicated to Prof. Ulrich Oberst on the occasion of his 70th birthday)
Proceedings of MTNS 2010, Budapest (Hungary)
also in: Algebraic Systems Theory, Behaviors, and Codes, E. Zerz (ed.), Shaker, Aachen, 2010, pp. 23-30
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Abstract:
Based on an extension of Stafford's classical theorem in noncommutative algebra Stafford (1978)
obtained in Coutinho, Holland (1988), the purpose of this paper is
to show that every controllable linear ordinary differential system with convergent power series
coefficients (i.e., germs of real analytic functions) and at least two inputs is differentially flat.
This result extends a result obtained in Quadrat and Robertz (2005),
Quadrat and Robertz (2007) for linear ordinary differential systems
with polynomial coefficients. We show how the algorithm developed in Quadrat and Robertz (2007)
for the computation of injective parametrizations and bases of free differential modules with
polynomial or rational function coefficients can be used to compute injective
parametrizations and flat outputs for these classes of differentially flat
systems. This algorithm allows us to remove singularities which naturally
appear in the computation of injective parametrizations and bases obtained by means of
Jacobson normal form computations.