A self-stabilizing system is one which can recover from transient faults in a nite number of steps. We present a theory for determining if a behavior speciication can be satissed with a self-stabilizing system and if not, then what the largest self-stabilizing subset and smallest self-stabilizing superset of the speciication is. The eeects of self-stabilizing behavior on the control of discrete...

A probabilistic self-stabilizing algorithm for a ring of identical processes is presented; the number of processes in the ring is odd, the processes operate synchronously, and communication is unidirectional in the ring. The normal function of the algorithm is to circulate a single token in the ring. If the initial state of the ring is abnormal, i.e. the number of tokens diiers from one, then e...

In this announcement, we report recent results where we address the open problem of snap-stabilization in messagepassing systems. (A full version of this paper is available as [3] at http://arxiv.org/abs/0802.1123.)

The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a small C1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stabilization condition by means of a boundary control, for ...