An exercise in proving self-stabilization through Lyapunov functions

Self-stabilizing distributed algorithms exhibit interesting analogies with the stabilizing feedback systems that are used in various engineering domains. In this paper, we show, with E.W. Dijkstra's (1974) token-ring algorithm for mutual exclusion serving as an example, that methodologies from control theory, e.g. Lyapunov's "second method", can be used to more easily and systematically prove the self-stabilization property of distributed algorithms.