On the Characteristic Equation and Minimal Realizations for Discrete-Event Dynamic Systems
Recently an analogy between conventional linear system theory and the relatively new theory on discrete-event dynamic systems has been shown to exist. The system descrip-tion in the new theory resembles the one of the conventional theory, provided that the operations addition and multiplication are replaced by maximization and addition respectively. One also speaks of a system in the max-algebra, which is a semi-ring. In this paper we investigate, by pursuing the analogy mentioned above, whether mini-mal realizations exist for discrete-event dynamic system if only the input/output description is given by means of the impulse response. A constuction procedure is suggested. It turns out that the characteristic equation of a matrix in the max-al-gebra (to be defined) plays a crucial rôle.
KeywordsImpulse Response Characteristic Equation Characteristic Polynomial Realization Theory Conventional Theory
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