Verification of Orbitally Self-Stabilizing Distributed Algorithms Using Lyapunov Functions and Poincare Maps

Authors:
Abhishek Dhama;Jens Oehlerking;Oliver Theel
Affiliations:
Carl von Ossietzky University of Oldenburg. Germany;Carl von Ossietzky University of Oldenburg. Germany;Carl von Ossietzky University of Oldenburg. Germany
Venue:
ICPADS '06 Proceedings of the 12th International Conference on Parallel and Distributed Systems - Volume 1
Year:
2006

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Abstract

Self-stabilization is a novel method for achieving fault tolerance in distributed applications. A self-stabilizing algorithm will reach a legal set of states, regardless of the starting state or states adopted due to the effects of transient faults, in finite time. However, proving self-stabilization is a difficult task. In this paper, we present a method for showing self-stabilization of a class of non-silent distributed algorithms, namely orbitally self-stabilizing algorithms. An algorithm of this class is modeled as a hybrid feedback control system. We then employ the control theoretic methods of Poincaré maps and Lyapunov functions to show convergence to an orbit cycle.