Verification of Orbitally Self-Stabilizing Distributed Algorithms Using Lyapunov Functions and Poincare Maps
Parallel and Distributed Systems, International Conference on (2006)
July 12, 2006 to July 15, 2006
Abhishek Dhama , Carl von Ossietzky University of Oldenburg. Germany
Jens Oehlerking , Carl von Ossietzky University of Oldenburg. Germany
Oliver Theel , Carl von Ossietzky University of Oldenburg. Germany
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 Poincar?e maps and Lyapunov functions to show convergence to an orbit cycle.
Fault Tolerance, Self-Stabilization, Verification, Hybrid Systems, Lyapunov Theory, Poincar?e maps
O. Theel, A. Dhama and J. Oehlerking, "Verification of Orbitally Self-Stabilizing Distributed Algorithms Using Lyapunov Functions and Poincare Maps," 12th International Conference on Parallel and Distributed Systems(ICPADS), Minneapolis, MN, 2006, pp. 23-30.