Relative Controllability of Hybrid Delay Multi-agent Systems

Abstract

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.