  Passive discrete-time systems in Pontryagin space setting are investigated.
In this case the transfer functions of passive systems, or characteristic
functions of contractive operator colligations, are generalized Schur
functions. The existence of optimal and *-optimal minimal realizations for
generalized Schur functions are proved. By using those realizations, a new
definition, which covers the case of generalized Schur functions, is given for
defects functions. A criterion due to D.Z. Arov and M.A. Nudelman, when all
minimal passive realizations of the same Schur function are unitarily similar,
is generalized to the class of generalized Schur functions. The approach used
here is new; it relies completely on the theory of passive systems.

Functional Analysis