Cluster consensus control for general linear systems with arbitrary convergence time

This paper investigates the cluster consensus prob-lem for general linear systems with arbitrary convergence time. By using the optimal control theory, we design a novel distributed controller with time-varying feedback gain for guaranteeing the cluster consensus can be reached within the pre-specified time. It is noteworthy that the underlying topology of each cluster is assumed to be directed graphs containing a directed spanning tree and the convergence time can be determined arbitrarily without depending on the initial condition or system parameters. Then, a rigorous analysis is provided to derive sufficient conditions in terms of topology structure. Finally, a numerical example is presented to validate the effectiveness of our result.