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Towards an “Erlangen program” for general linear systems theory

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Computer Aided Systems Theory — EUROCAST '91 (EUROCAST 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 585))

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Abstract

Any generalizing theory will have scientific and practical validity only if it:

  1. 1.

    reduces theoretical complexities in special theories caused by some inherent limitations;

  2. 2.

    contains special theories as special cases, moreover results, obtained beforehand, must be reproduced in a new more wider scale;

  3. 3.

    brings to appearing of new theoretical results, which are impossible in special theories, moreover, it gives other new questions and problems then solves the old ones;

  4. 4.

    gives the new effective analysis methods and algorithms for the solution of important practical problems.

Does the given algebraic signals theory satisfy these demands? To answer the question, let's analyze what is done in its scale.

Firstly, a fundamental theoretical scheme is designed, containing the problems and research subject description and in which the main theory principles are proved on an abstract level. Secondly, sufficiently common and effective mathematical method of harmonic analysis of signals and systems known models have been worked out. Thirdly, a valuable range of new special theories have been worked out in detail put into the base of the most important practical problems solution.

Such a state of signals and systems abstract theory shows the principle completion of its construction. Hence the following its development must be connected with generalized harmonic analysis methods to concrete problems solution. The obtained practical results will give the answer to the question about the worked out theory and its applicability limits.

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Authors and Affiliations

  1. Institute of Algorithms and Cognitive Systems, University of Karlsruhe, Am Fasanengarten 5, P. O. Box 6980, D-7500, Karlsruhe 1

    R. Creutzburg

  2. Faculty of Radioelectronics Department of Automatics and Telemechanics, Ural Polytechnical Institute, SU-620002, Sverdlovsk, Soviet Union

    V. G. Labunets & E. V. Labunets

Authors
  1. R. Creutzburg
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  2. V. G. Labunets
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  3. E. V. Labunets
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Franz Pichler Roberto Moreno Díaz

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Creutzburg, R., Labunets, V.G., Labunets, E.V. (1992). Towards an “Erlangen program” for general linear systems theory. In: Pichler, F., Díaz, R.M. (eds) Computer Aided Systems Theory — EUROCAST '91. EUROCAST 1991. Lecture Notes in Computer Science, vol 585. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021003

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