Characterization of Transfer Functions of Pritchard–Salamon or Other Realizations with a Bounded Input or Output Operator

Abstract

We show that the transfer functions that have a (continuous-time) well-posed realization with a bounded input operator are exactly those that are strong-H 2 (plus constant feedthrough) over some right half-plane. The dual condition holds ifi the transfer function has a realization with a bounded output operator. Both conditions hold ifi the transfer function has a Pritchard{ Salamon (PS) realization. A state-space variant of the PS result was proved already in (3), under the additional assumption that the weighting pattern (or impulse response) is a function (whose values are bounded operators). We illustrate by an example that this does not cover all PS systems, not even if the input and output spaces are separable. Mathematics Subject Classiflcation (2000). Primary 93B15, 93B28; Secondary 47B35.