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.