Robust distributed consensus on the median value for networks of heterogeneously perturbed agents

The problem of how to force the states of a network of non-identical systems to converge on a predefined function of the their initial conditions is a problematic challenge because of unknown perturbations or unmodeled dynamics shift the equilibrium of the network with respect to the expected 'nominal' one. Furthermore, whenever outlier agents are considered, the well-studied averaged estimation of the agents initial conditions which find application in several field is definitely compromised due to the fragility of the mean statistical measure. In light of these considerations, in this paper we show how the integral sliding-mode control design paradigm can be usefully applied in the framework of multi-agent systems to solve the consensus on the median value problem for a network of perturbed non-identical single integrators. Lyapunov analysis is presented to support the convergence properties of the algorithm, and simulative results are discussed to corroborate the theoretical result.