The class of pseudorational transfer functions consists, roughly speaking, of the ratio of entire functions of exponential type that are Laplace transforms of distributions with compact support. This class gives a convenient platform for dealing with distributed systems whose state space is determined by bounded-time data. Delay-differential systems are typical examples. The following appealing features are known: Starting from a completely general input/output framework, this class allows a concrete realization procedure based on the above fractional representation of transfer functions (or impulse responses). It is then also possible to give a complete characterization of spectral properties of such realizations. Such spectral properties allows us to give a stability criterion and also an appropriate relationship between internal and external stability notions. Based on a concrete representation of the state space, it also leads to a concrete characterization of left-shift invariant subspaces of H 2 . This result has a direct consequence on H infin  control theory. We give a concise yet comprehensive and unified overview of such results. The paper is concluded with this and also a recent result on the existence of a Bezout identity in this class.
['Yutaka Yamamoto']
Pseudorational transfer functions—A survey of a class of infinite-dimensional systems