Fault-tolerant stabilisation in double-integrator networks

The paper considers a network of agents with double-integrator internal dynamics, which share pieces of information on their position states. For such a system, a fault-tolerant decentralised stabilisation problem is addressed. The goal consists in placing the closed-loop poles in the open left-half of the complex plane, even in the presence of faults of the transmitting and receiving apparatuses of one or more agents. By exploiting some previous results on fault-tolerant control, a necessary and sufficient condition for the problem to admit a solution is proved. Further, an explicit formula is given for the local regulators, which can be taken of the first order, actually the least one. Finally, the theory is extended to networks of agents with multiple-integrator internal dynamics.