Fault-tolerant Stabilization in Discrete-time Multiple-integrator Networks

The paper addresses a fault-tolerant decentralized stabilization problem for a network of agents which have discrete-time multiple-integrator internal dynamics and share information on their states according to an arbitrary topology. The specific goal consists in placing the eigenvalues inside the open unit disk, even in the presence of faults of the transmitting and receiving apparatuses of one or more agents. For this problem, a necessary and sufficient solvability condition is presented, together with explicit formulas for a class of regulators, some of which are of least order.