  Recent work of the operator algebraists P. Muhly and B. Solel, primarily
motivated by the theory of operator algebras and mathematical physics,
delineates a general abstract framework where system theory ideas appear in
disguised form. These system-theory ingredients include: system matrix for an
input/state/output linear system, Z-transform from a "time domain" to a
"frequency domain", and Z-transform of the output signal given by an
observation function applied to the initial condition plus a transfer function
applied to the Z-transform of the input signal. Here we set down the
definitions and main results for the general Muhly-Solel formalism and
illustrate them for two specific types of multi-dimensional linear systems: (1)
dissipative Fornasini-Marchesini state-space representations with transfer
function equal to a holomorphic operator-valued function on the unit ball in
${\mathbb C}^d$, and (2) noncommutative dissipative Fornasini-Marchsini linear
systems with evolution along a free semigroup and with transfer function
defined on the noncommutative ball of strict row contractions on a Hilbert
space.
