Fault-tolerant pole-placement in single-integrator networks

The paper faces a fault-tolerant control problem for a network of agents with single-integrator internal dynamics, which share information on their states according to an arbitrary topology. Specifically, we aim at designing a decentralized regulator able to place the closed-loop dominant poles near prespecified locations. Furthermore, this goal has to be achieved even in the presence of faults of the transmitting and receiving apparatuses of the single agents. We prove a necessary and sufficient solvability condition for our pole-placement problem, and show that it can be solved if and only if a simpler fault-tolerant stabilization problem admits a solution. Then, we give an explicit formula for a class of possible regulators.