Attack detection in a cluster divided consensus network

We consider the problem of attack detection, isolation and counterattack in a network of agents. This particular network is divided into several smaller networks, which are disconnected from each other. The states continuously evolve following a linear consensus protocol and approach local agreements specific to each sub-network/cluster. So the agents are capable of achieving global consensus, at a given instant one agent from each sub-network, called leader, updates its state. Our objective here, to be more specific, is to develop a bank of unknown input observers (UIOs) such that each agent can monitor its own output link and detect if a neighbor is being attacked. Moreover, these observers should also be able to estimate the attack value and respond with a counter-attack to keep the global consensus from diverging too far from the expected global consensus value. We provide LMI sufficient conditions for the design of the bank of observers. Simulations are presented to illustrate our results.