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On an algebraic theory of systems defined by convolution operators

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Abstract

For a large class of linear continuous-time systems including delay-differential systems, an algebraic theory is presented in terms of Noetherian operator rings generated from a finite number of elements belonging to a convolution algebra of distributions. The external behavior of these systems is given by a finite set of input/output (convolution) operator equations which are solved in a novel manner by constructing an operational transfer function matrix and then applying an extension of the Mikusiński operational calculus. After the formulation of an internal representation consisting of a finite set of scalar operational-differential equations, the problem of realizing an operational transfer function matrix by such an internal description is considered. Results on the existence and construction of realizations are given.

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Authors and Affiliations

  1. School of Electrical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA

    E. W. Kamen

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  1. E. W. Kamen
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Additional information

This work was supported by the NSF under Grant No. GK-32697.

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Kamen, E.W. On an algebraic theory of systems defined by convolution operators. Math. Systems Theory 9, 57–74 (1975). https://doi.org/10.1007/BF01698126

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  • DOI: https://doi.org/10.1007/BF01698126

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