Containment Control of Fractional-Order Networked Systems With Time-Varying Communication Delays: A Positive System Viewpoint

This work deals with the containment control problem of multi-agent networks with different fractional-order dynamics under bounded communication delays. Unlike most existing work, we analyze this problem from a positive system viewpoint. For the case where the communication delays are the same constant, we investigate the entry-wise monotonicity of the solution of the corresponding error system. Then, by bounding the solution of the time-varying delay system by its corresponding system with constant delay, it is shown that as long as every follower can obtain information at worst from one leader directly or indirectly, the followers will finally arrive at the convex hull spanned by the stationary leaders. Our results reveal that the communication delay independence in containment control of fractional-order multi-agent networks has a strong connection with the delay-insensitive stability of positive systems. An example is also employed to illustrate the obtained theoretical findings.