A note on finite memory in locally square integrable systems

In the past decade J.C. Willems has developed the notion of the behavior of a system: the behavior of a system is the set of trajectories satisfying the system laws. He has studied especially linear time invariant discrete time systems in great detail. In this paper we concentrate on continuous time systems, in particular we study a class of locally square integrable systems and we investigate whether closed. linear, time invariant systems have finite memory.