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Evaluation of matrix polynomials in the state companion matrix of linear time invariant systems

Evaluation of matrix polynomials in the state companion matrix of linear time invariant systems
Evaluation of matrix polynomials in the state companion matrix of linear time invariant systems
In this paper a new iterative algorithm is presented for the numerical evaluation of matrix polynomials in the state companion matrix of a linear time invariant system. The algorithm also enables the polynomial coefficients of the characteristic equation and the eigenvectors of the state companion matrix to be found. In particular, a truncated series approximation is given for the state transition matrix, providing the most efficient computation known for a prescribed truncation error. The adjustment recursive coefficients used in evaluating the state transition matrix are shown to be on alternative means of evaluating the elements of the inverse Vandermonde matrix of the systems' eigenvalues.
0020-7721
301-307
Harris, C J
c4fd3763-7b3f-4db1-9ca3-5501080f797a
Harris, C J
c4fd3763-7b3f-4db1-9ca3-5501080f797a

Harris, C J (1973) Evaluation of matrix polynomials in the state companion matrix of linear time invariant systems. International Journal of Systems Science, 4 (3), 301-307. (doi:10.1080/00207727308920016).

Record type: Article

Abstract

In this paper a new iterative algorithm is presented for the numerical evaluation of matrix polynomials in the state companion matrix of a linear time invariant system. The algorithm also enables the polynomial coefficients of the characteristic equation and the eigenvectors of the state companion matrix to be found. In particular, a truncated series approximation is given for the state transition matrix, providing the most efficient computation known for a prescribed truncation error. The adjustment recursive coefficients used in evaluating the state transition matrix are shown to be on alternative means of evaluating the elements of the inverse Vandermonde matrix of the systems' eigenvalues.

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Published date: 1973
Additional Information: Address: London
Organisations: Southampton Wireless Group

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Local EPrints ID: 252052
URI: http://eprints.soton.ac.uk/id/eprint/252052
ISSN: 0020-7721
PURE UUID: 1140f97a-8766-42b2-ba8c-87ce0178eff0

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Date deposited: 03 Dec 1999
Last modified: 16 Mar 2024 22:48

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Author: C J Harris

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