Raimund Ober and Stephen Montgomery-Smith, Bilinear Transformation of Infinite-Dimensional State-Space Systems and Balanced Realizations of Nonrational Transfer Functions.
SIAM J. Control Optim. 28(2) (1990), 438-465.
The bilinear transform maps the open right half plane to the open unit disk and is therefore a suitable tool for carrying over results for continuous-time systems to discrete-time systems and vice versa. Corresponding state-space formulae are widely used and well understood for the case of finite-dimensional systems. In this paper infinite-dimensional generalizations of these formulae are studied for a general class of infinite-dimensional state-space systems. In particular, it is shown that reachability and observability are carried over and that the reachability and observability gramians are preserved under this transformation. Young showed that a wide class of nonrational discrete-time transfer functions admit a balanced state-space representation. It is shown that this result carries over to the continuous-time situation via the bilinear transformation.
List of all preprints