Convex analysis and spectral analysis of timed event graphs

Using the algebra of diodes, the analogy between timed event graphs and conventional linear systems is examined by showing that some periodic inputs of the former behave as cosine inputs for the latter. In particular, a meaning is given to such notions as 'phase shift' and 'amplification gain', which allow the Black and Bode plots to be discussed for discrete-event systems. In this theory, classical concepts of convex analysis such as inf-convolution and Fenchel conjugate play the parts that convolution and the Laplace transform play in the conventional case.<>