A New Verification Technique for Self-Stabilizing Distributed Algorithms based on Variable Structure Systems and Ljapunov Theory

A particularly suitable design strategy for constructing a robust distributed computer application is to endow it with a self-stabilization property. Such a property guarantees that the system will always return to and stay within a specified set of legal states within bounded time regardless of its initial state. A self-stabilizing application therefore has the potential of recovering from the effects of arbitrary transient failures. However, to actually prove that an application self-stabilizes can be quite tedious with current verification methodologies and is non-trivial. The self-stabilizing property of distributed algorithms exhibits interesting analogies to stabilizing feedback systems used in various engineering domains. In this paper we show that methodologies from control theory can be used to more easily prove the selfstabilization property of distributed algorithms.