A New Framework on Controllability of the Second-Order Multiagent Systems Under Fixed and Switching Topologies

This article presents a new framework for the controllability of the second-order multiagent systems under fixed and switching topologies. With the neighbor-based protocol adopted, the multiagent systems under fixed topology are transformed into a second-order time-invariant system. The solution of the system is obtained by using the Wronskian technique and a series of criteria for the controllability of the system are established. For the multiagent systems under switching topologies, a second-order switched system is obtained by applying the time-varying protocol. An explicit solution of the system is presented by constructing a new nested function and a Gramian-type criterion on the controllability of the system is established. On this basis, a new nested subspace is constructed, which turns out to be equivalent to the controllable state set of the system. Several examples are provided to demonstrate the effectiveness of the theoretical results.