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Multidimensional constant linear systems. (English) Zbl 0715.93014
From the text: The starting point for this work was the paper of J. C. Willems [Automatica, 22, 561-580 (1986; Zbl 0604.62090)]. Whereas the techniques used in this paper are new for system theory as far as I (the author) know, the basic notions and the formulation of many results are derived from the one-dimensional models as, hopefully, every system theorist can realize.
The following subjects are treated: input-output structures of systems and their transfer matrix, signal flow spaces and graphs of systems and block diagrams, transfer equivalence and (minimal) realizations, controllability and observability, rank singularities and their connection with the integral representation theorem, invertible systems, the constructive solution of the Cauchy problem and convolutional transfer operators for discrete systems.
Reviewer: J.W.Nieuwenhuis

93B25 Algebraic methods
93C05 Linear systems in control theory
39A10 Additive difference equations
93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
44A40 Calculus of Mikusiński and other operational calculi
93B07 Observability
94C99 Circuits, networks
44A55 Discrete operational calculus
93B15 Realizations from input-output data
35E20 General theory of PDEs and systems of PDEs with constant coefficients
93C35 Multivariable systems, multidimensional control systems
93B20 Minimal systems representations
35N05 Overdetermined systems of PDEs with constant coefficients
Full Text: DOI
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