Abstract: Concerning a class of discrete-event systems in Z-domain, rational expressions based on minimax algebra are introduced as a simple way for formulating transfer functions, which are infinite formal series by definition. A rational expression is transformed into sum of generalized fractions in design and analysis of a system. Reduction of a generalized fraction is discussed and its standard form given. Spectrum characteristics of a rational transfer function is studied with its connection to periodic response of the system. Applications such as minimal realization and optimal control are illustrated with an example.