Admissibility of Unbounded Control Operators

For linear systems described by x (t) = Ax (t) + Bu (t), where A generates a semigroup on the state space X and B is an unbounded operator, some necessary as well as some sufficient conditions are given for B to be admissible, i. e. , for any t, the state x (t) should be in X and should depend continuously on the input u Lᵖ. This approach begins with an axiomatic description of such a system in terms of a functional equation. The results are applied to the wave equation on a bounded interval.