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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This research was supported in part by US Army Research Grant DAA 29-77-G-0225 and US Air Force Grant AFOSR 76-3034 Mod.B while the author was at the Center for Mathematical System Theory, University of Florida, Gainesville, FL 32611, USA.
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Yamamoto, Y. Realization theory of infinite-dimensional linear systems. Part II. Math. Systems Theory 15, 169–190 (1981). https://doi.org/10.1007/BF01786978
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DOI: https://doi.org/10.1007/BF01786978