Tellegen's principle, non-minimal realization of systems and inversion of polynomial Vandermonde matrices (Q2882912)
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scientific article; zbMATH DE number 6032986
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Tellegen's principle, non-minimal realization of systems and inversion of polynomial Vandermonde matrices |
scientific article; zbMATH DE number 6032986 |
Statements
11 May 2012
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Vandermonde matrix inversion
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Kalman's duality
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Tellegen's principle
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signal flow graphs
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inversion algorithm
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polynomial Vandermonde matrix
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numerical experiments
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Gauss-Jordan method
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Tellegen's principle, non-minimal realization of systems and inversion of polynomial Vandermonde matrices (English)
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The authors study the relationship between the following concepts: (1) Electrical Engineering -- inversion of a signal flow graph, (2) Computer Science -- Tellegen's principle, and (3) Linear Algebra -- inversion of a polynomial Vandermonde matrix. They establish the connection between Kalman's duality and Tellegen's principle. This fact is used to prove the duality theorem for the case of the non-minimal realization of a system. They develop a procedure, which for any given system of polynomials leads to an inversion algorithm for the corresponding polynomial Vandermonde matrix. The results of preliminary numerical experiments with the proposed algorithm are given. The code for the numerical experiments is written in MATLAB, for the Gauss-Jordan method.
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