Abstract
This paper studies the real-time behavior of constant linear systems. A function space Λ is introduced to give a precise language to discuss the working mode of systems. It is shown that a realization of a constant linear input/output map produces the desired outputs during the application of inputs. A differential equation description is derived for those systems whose weighting patterns are sufficiently smooth. The notion of topological observability in bounded time yields a necessary and sufficient condition under which the canonical realization of a constant linear input/output map has a Banach state space.
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