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.
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.