This paper considers relative controllability of leader-follower hybrid
delay multi-agent systems under fixed communication topology, where two
kinds of state delays are existed and each agent subjects to one of
them. Some agents with unidirectional signal flows are assigned as
leaders and the others are followers. With neighbor-based protocols
adopted, the multi-agent systems are represented as a higher dimensional
two-delay system without pairwise matrices permutation. Fundamental
solution matrix of the two-delay system is constructed by improving the
methods in literature, further solution of the system is obtained. Based
on the solution Gramian criterion on relative controllability of the
system is established. Whereafter, a sufficient condition on relative
controllability of the system is presented. An example is attached to
support the work.