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Zbl 0802.93027
El Asmi, S.; Fliess, M.
Inversion formulas. (Formules d'inversion.) (French)
[A] Bonnard, Bernard (ed.) et al., Analysis of controlled dynamical systems. Proceedings of a conference held in Lyon, France, July 1990. Boston, MA: Birkhäuser. Prog. Syst. Control Theory. 8, 201-210 (1991). ISBN 0-8176-3576-9

Recently, the second author gave a new mathematical interpretation of invertibility: a system is left invertible if each variable (of the system) except output variables satisfies a differential algebraic equation with coefficients depending on the output [the second author, Forum Math., 1, No. 3, 227-238 (1989; Zbl 0701.93048)]. He also defined the output differential rank of a system $[u\sb 1,\dots,u\sb m,y\sb 1,\dots,y\sb p]$ (linear or nonlinear) in such a way that this rank is $m$ if and only if the system is left invertible.\par In the paper under review, the authors give explicit formulas for this rank using classical results of dimension theory in algebra (existence of Hilbert's characteristic polynomials). They also show that some previous results on invertibility of some systems by Grasse, Sain and Massey, Nijmeijer and others are particular cases of their general approach.
[Ch.Michaux (Mons)]

MSC 2000:: *93B99 Controllability, observability, and system structure
12H05 Differential algebra
93C20 Control systems governed by PDE

Keywords: invertibility; Hilbert's characteristic polynomials

Citations: Zbl 0701.93048

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