)>IJH=?J In this paper we present a decentralized algorithm to estimate the eigenvalues of the Laplacian matrix that encodes the network topology of a multi-agent system. We consider network topologies modeled by undirected graphs. The basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the Laplacian matrix. In this way, the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the nite number of frequencies at which the signal oscillates.

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In this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous-time first-order integrator dynamics affected by bounded disturbances. The topology of the network is described by a directed graph. The proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time. An upper bound to the convergence time is explicitly derived in the technical note. Simulation results, referring to a network of coupled Kuramoto-like oscillators, are illustrated to corroborate the theoretical analysis.

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In this paper we propose a novel continuous-time protocol that solves the consensus problem on the median value, i.e., it provides distributed agreement in networked multi-agent systems where the quantity of interest is the median value of the agents' initial values. In contrast to the average value, the median value is a statistical measure inherently robust to the presence of outliers, which is a significant robustness issue in large-scale sensor and multi-agent networks. The proposed protocol requires only binary information regarding the relative state differences among the neighboring agents and achieves consensus on the median value in finite time by exploiting a suitable ad-hoc discontinuous local interaction rule. In addition, we characterize certain resiliency properties of the proposed protocol against the presence of uncooperative agents which do not implement the underlying local interaction rule whereas they interact with their neighbors thus influencing the network. In particular, we prove that despite the persistent influence of (at most) a certain number of uncooperative agents, the cooperative agents achieve finite time consensus on a value lying inside the convex hull of the cooperative agents' initial conditions, provided that the special class of so-called "k-safe" network topology is considered. Capabilities of the proposed consensus protocol and its effectiveness are supported by numerical studies.