Fault-tolerant stabilization of multiple-integrator networks with general information sharing

The paper considers a network of agents with identical multiple-integrator dynamics. The agents share information according to an arbitrary topology. The information is relative to the states corresponding to some of the highest integration levels. With reference to this setting, a decentralized stabilization problem is faced, under the additional assumption that faults may occur in the communication apparatuses of one or several of the agents. Necessary and sufficient solvability conditions are presented for the problem, together with explicit formulas for a class of regulators, some of which are least-order.