Asymptotic Behavior of the Attainable Sets of Linear Periodic Control Systems

This paper deals with the attainable sets of linear periodic control systems. The asymptotic behavior of the attainable sets over a long time interval is investigated in terms of shapes of the sets. The shape of a set stands for the totality of all its images under nonsingular linear transformations. It is shown that there exist limits of the shape of attainable sets corresponding to time instants with the same residue modulo the period of the system and that the limit shapes are different if the system includes a stable subsystem.