Controllability of linear discrete‐time multi‐agent systems with delay in states

Abstract This article investigates the controllability of discrete‐time multi‐agent systems with leader‐follower structure. A discrete‐time multi‐agent systems with dual state delays is investigated, and an absolute communication control protocol is proposed. The representation solution of the model under matrix commutativity is derived by utilizing the discrete matrix delayed exponential associated with double delays. Furthermore, the Gramian matrix and the control function determined by the discrete matrix delayed exponential are constructed. Controllability criteria for the linear discrete‐time multi‐agent systems are generated. Finally, numerical simulations are conducted to verify the accuracy of the theoretical results.