Quaestiones Mathematicae

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On the unboundedness of control operators for bilinear systems

Abdelalli Idrissi


The aim of this work is to study the classes of unbounded linear
control operators which ensure the existence and uniqueness of the mild and
strong solutions of certain bilinear control systems. By an abstract approach,
similar to that adopted by Weiss [18], we obtain a connection between these
classes and those constituted by control operators with values in the
extrapolation space associated to the state space. We show the localization of
these classes and, in certain cases, the identification with concrete spaces.

Mathematics Subject Classification (2000): 93C25, 47D03, 93B28.

Key words: Bilinear control system; semigroup; unbounded control operator;
extrapola­tion space; Favard class.

Quaestiones Mathematicae 26(2003), 105-123.
AJOL African Journals Online