8.1 Irreducible (Minimal) Realizations The internal structure of
a system may allow some of the integrators (or delay elements)
to be shared by several input-output pairs and still result in
the same transfer matrix. The system that realizes the maximum
possible degree of sharing (and, consequently, the smallest
possible dimension of the associated state space) is called the
irreducible (or minimal) realization (see, e.g., Brogan (1991),
Section 12.4). The function MinimalRealization tries to find
such a realization. Finding the irreducible (minimal)
realization. The input system for MinimalRealization can be in
either state-space or transfer function form; the resultant
system is always a state-space one. For SISO transfer function
systems, MinimalRealization constructs a state-space realization
after an attempt to cancel common pole-zero pairs (the
underlying function, PoleZeroCancel, can also be accessed
directly, see Section 8.6). Otherwise, MinimalRealization
constructs a state-space realization first an