Minimal state space realization of SISO systems in the max algebra

B. De Schutter and B. De Moor, "Minimal state space realization of SISO systems in the max algebra," Tech. rep. 93-57, ESAT-SISTA, K.U.Leuven, Leuven, Belgium, 31 pp., Oct. 1993.

First we determine necessary and for some cases also sufficient conditions for a polynomial to be the characteristic polynomial of a matrix with elements in Rmax. Then we indicate how to construct a matrix such that its characteristic polynomial is equal to a given monic polynomial in Smax, the extension of Rmax. Next we use these results to develop a procedure to find the minimal state space realization of a single input single output (SISO) discrete event system, given its Markov parameters.

 * Technical report: pdf file (283 KB)
      Note: More information on the pdf file format mentioned above can be found here.

Bibtex entry:

        author={B. {D}e Schutter and B. {D}e Moor},
        title={{Minimal} state space realization of {SISO} systems in the max algebra},
        institution={ESAT-SISTA, K.U.Leuven},
        address={Leuven, Belgium},

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