Minimal realization in linear system of max-algebra

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Authors: Sun, Z.M., Chen, W.D. and Yu, H.N.

Journal: Kongzhi yu Juece/Control and Decision

Volume: 21

Issue: 5

Pages: 521-526

ISSN: 1001-0920

The minimal realization of a low dimensional SISO linear system in the max-algebra is studied. The necessary and sufficient condition for the existence of 2-dimensional minimal realization is given, which is described by the relation of elements of the infinite sequence and is easy to check. The method of constructing a 2-dimension minimal realization is presented through the structural standardization and arithmetic of minimal realization developed by Fengsheng Tu, by which the problem of 2-dimension minimal realization is solved completly. Consequently it is proved that the conjecture of Fengsheng Tu is right with the dimension of the minimal realization no more than 2. Finally, a counter-example shows that the Fengsheng Tu conjecture dose not hold with the dimensions of minimal realization bigger than 2.

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