Abstract
We study linear control systems with unbounded control and observation operators using certain regularization techniques. This allows us to introduce a modification of the transfer function for the system even if the input and output operators are not admissible in the usual sense. The modified transfer function is utilized to show exponential stability of sufficiently smooth solutions for the internal system under appropriate admissibility conditions on the system operators and appropriately modified stabilizability and detectability assumptions. If the internal system satisfies additional, yet common, regularity properties, then its uniform exponential stability is obtained.
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