Minimal realizations and state space transformations in the symmetrized max-algebra

Reference:
R. de Vries, B. De Schutter, and B. De Moor, "Minimal realizations and state space transformations in the symmetrized max-algebra," Tech. rep. 97-84, ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 21 pp., Dec. 1997.

Abstract:
Similarity transformations between two different minimal realizations of a given impulse response of a discrete event system are discussed. In the symmetrized max-algebra an explicit expression can be given for the transformation between an arbitrary minimal realization of a given impulse response and a minimal realization of the same impulse response in a standard form. It is conjectured that a more general result holds which gives a transformation matrix between any two minimal realizations of an impulse response. We will illustrate the difficulties encountered when trying to prove this conjecture.

Downloads:

Technical report: pdf file (169 KB)
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Bibtex entry:

@techreport{deVDeS:97-84,
        author={R. de Vries and B. {D}e Schutter and B. {D}e Moor},
        title={Minimal realizations and state space transformations in the symmetrized max-algebra},
        number={97-84},
        institution={ESAT-SISTA, K.U.Leuven},
        address={Leuven, Belgium},
        month=dec,
        year={1997}
        }

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