Consensus control of linear second-order discrete-time systems with guaranteed rate of convergence

This paper presents necessary and sufficient conditions which guarantee consensus for a homogeneous network of linear second-order discrete-time systems. The eigenvalues of the graph Laplacian can be complex. Linear controllers which achieve consensus with a guaranteed rate of convergence are presented. The paper concludes with an example where the proposed controllers synchronize a network of discrete-time double integrators with several different convergence rates.