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Extension Modules in Behavioral Linear Systems Theory

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Abstract

For certain signal spaces, the algebraic concept of extension modules yields a full classification of system theoretic properties such as controllability and autonomy. The present paper summarizes the results of various authors on the subject, and unifies them in the language of extension modules. The computation of extension modules is based on the computation of syzygies (i.e., kernels of module homomorphisms). This can be done constructively, using the theory of Gröbner bases.

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Authors and Affiliations

  1. Department of Mathematics, University of Kaiserslautern, 67663, Kaiserslautern, Germany

    Eva Zerz

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  1. Eva Zerz
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Zerz, E. Extension Modules in Behavioral Linear Systems Theory. Multidimensional Systems and Signal Processing 12, 309–327 (2001). https://doi.org/10.1023/A:1011905623429

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