2006•Kongzhi yu jueceRequires access
Minimal Realization in Linear System of Max-algebra
Zhimin Sun
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Abstract
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 conjecture of Fengsheng Tu dose not hold with the dimensions of minimal realization bigger than 2.