Abstract
The goal of this paper is to advertise the tight links between the theory of Discrete-Event Systems and Path-Complete Lyapunov Functions. These are algebro-combinatorial stability criteria for hybrid systems, whose meta-parameters are an automaton and a template of candidate Lyapunov functions.To do this, we analyse a phenomenon recently observed in the literature, namely the statistical ordering of Path-Complete Lyapunov Functions, which is by far not well understood yet: Path-Complete Lyapunov functions can be endowed with a preorder structure with respect to their performance. It has been recently shown that the preorder corresponding to relative worst case performance can be characterized with tools from automata theory, but the ordering corresponding to statistical relative performance has remained elusive. We advocate for a Discrete-Event Systems approach to this problem and provide preliminary results in this direction.
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