M. Fliess et R. Hotzel, ON LINEAR-SYSTEMS WITH A DERIVATION OF NONINTEGER ORDER, Comptes rendus de l'Academie des sciences. Serie II. Mecanique, physique, chimie, astronomie, 324(2), 1997, pp. 99-105
Controllability observability and realization properties of linear sys
tems with a derivation of non-integer order, which were introduced in
control theory and signal processing by A. Oustaloup, are examined in
the more general framework of systems over a ring of operators. A char
acterization of input-output stability makes it possible to construct
controllers of non-integer order.