Based on a recent convex programming algorithm for simultaneous stabilization by linear state feedback, we propose two types of control law for stabilizing a family of systems, when either a simultaneously stabilizing state feedback gain or a simultaneously stabilizing output injection matrix exists, and complete state information is not available. The proposed control laws are illustrated by a...

In this paper, we investigate the possibility to deterministically solve the gathering problem (GP) with weak robots (anonymous, autonomous, disoriented, deaf and dumb, and oblivious). We introduce strong multiplicity detection as the ability for the robots to detect the exact number of robots located at a given position. We show that with strong multiplicity detection, there exists a determini...

We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity-mismatch in the intrinsic firing rate of the neurons-can stabilize the phase locking and lead to more precis...

In this paper, we mix two well-known approaches of the fault-tolerance: robustness and stabilization. Robustnessis the aptitude of an algorithm to withstand permanent failures such as process crashes. The stabilization is a generaltechnique to design algorithms tolerating transient failures. Using these two approaches, we propose algorithms thattolerate both transient and crash fail...

Certain types of system faults, notably data errors due to transient faults, can be repaired by software. The repair consists of identifying faulty variables and then rewriting data to correct the fault. If fault identiication is imprecise, repair procedures can contaminate non faulty processes from data originating at faulty processes. This contamination danger is resolved by delaying data cor...

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slo...

We present the first self-stabilizing consensus and replicated state machine for asynchronousmessage passing systems. The scheme does not require that all participants make a certain numberof steps prior to reaching a practically infinite execution where the replicated state machine exhibitsthe desired behavior. In other words, the system reaches a configuration from which it operat...

Virtual synchrony (VS) is an important abstraction that is proven to be extremely useful when implemented over asynchronous, typically large, message-passing distributed systems. Fault tolerant design is critical for the success of such implementations since large distributed systems can be highly available as long as they do not depend on the full operational status of every system participant...

An edge-weighted graph G = (V,E) is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as network bargaining games and cooperative matching games, because they characterize instances which admit stable outcomes. Motivated by this, in the last few yea...