Integral sliding modes for the robustification of consensus-based multi-agent based systems

The problem of enforcing the state variables of a network of heterogenous dynamical systems to agree on a predefined function of the corresponding initial conditions (e.g., the average value) is a problematic challenge when perturbations affect agents' dynamics. When the linear consensus algorithms are used, such uncertainties shift the equilibrium of the network with respect to the expected nominal one. Thus motivated, 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-average problem for a network of heterogenous agents with perturbed integrator dynamics. Lyapunov analysis is developed to support the convergence properties of the proposed algorithm, and simulative results are discussed to corroborate the theoretical results.