On the reduced conditions for positive consensus of second‐order multi‐agent systems

Abstract

This paper investigates the reduced conditions for positivity‐preserving consensus of positive multi‐agent systems with second‐order dynamics. The solvability of the positive consensus problem (PCP) is discussed under both undirected and directed topologies, which is related to the positive stability of each agent's dynamics. Necessary and sufficient conditions are presented for continuous‐time and discrete‐time cases to solve PCP over undirected graphs. When the graph is directed, sufficient conditions for the problem solvability and a Schur stability testing method for second‐order complex matrices are provided, where the traditional Routh‐Hurwitz criteria (Jury criteria) is not suitable. Some numerical examples are presented to illustrate the theoretical results.