Fault Tolerant Stabilizability of MIMO Multi-Hop Control Networks

A MIMO Multi-hop Control Network (MCN) consists of a MIMO LTI plant where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network and data flow is performed using scheduling and routing of sensing and actuation data. We explicitly characterize by means of necessary and sufficient conditions the set of network configurations that invalidate controllability and observability of the plant. We show that checking such necessary and sufficient conditions can be solved with a complexity that is combinatorial with respect to the number of input and output signals. To overcome this difficulty, we propose an efficient algorithm to design the network configuration in linear time still guaranteeing controllability and observability.