Abstract
In this paper, we develop new bounding methodologies of max-plus linear systems inspired by results dealing with comparison of stochastic processes. The methods developed in this paper are based on preorder and monotonicity. These methods allow us to obtain comparisons of timed event graphs (TEGs) by comparing their dater dynamical equations. We illustrate with a simple example of Baccelli and Hong (2000) that part of the results provides new approach for computing lower and upper bounds of the Lyapunov exponent of discrete event systems (DES). However the problem of the computation of bounds on Lyapunov exponent requires thorough investigations which are beyond the scope of this work.
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