r ‐consensus control for discrete‐time high‐order multi‐agent systems

This study considers a consensus problem of discrete‐time high‐order multi‐agent systems with digraph. A concept r ‐consensus for discrete‐time multi‐agent systems is introduced, and consensus protocols are proposed for solving such problems. A sufficient and necessary condition for r ‐consensus is obtained using matrix theory. As a special case, criteria of r ‐consensus for third‐order systems are given, in which the exact relationship of feedback parameters is established. Finally, the effectiveness of the theoretical results is demonstrated through a numerical simulation.