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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 &#x201c;time domain&#x201D; to a &#x201C;frequency domain&#x201D;, 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 multidimensional linear systems: (1) dissipative Fornasini-Marchesini state-space representations with transfer function equal to a holomorphic operator-valued function on the unit ball in &#x2102;<sup>d</sup>, 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.

A W*-correspondence approach to multi-dimensional linear dissipative systems