Fractional-order controllability of multi-agent systems with time-delay

Generally, nature is understood and explored from the point of view of integer order, however, lots of physical systems in complex practical environments can exhibit the fractional-order (non-integer order) dynamics, which can better reveal the essential properties, behaviors and the law of basic development. A novel fractional-order model with time-delay is built and the fractional-order controllability problem of networked multi-agent systems (MASs) is discussed. Comparing with the integer-order controllability problem for MASs, the fractional-order controllability problem of MASs not only needs to consider the dynamics of the agent itself, the communication and connection between the agents and the protocols followed by the evolution of the agent undefined state, but also to consider the order number of MASs. It is also shown that the fractional-order controllability of MASs with time-delay only lies on the communication interaction from the leaders to followers and the order number of such system, but time-delay has no effect on the controllability via the controllable rank criterion. Some computationally efficient conditions of the fractional-order controllability for MASs with time-delay are obtained based on fixed and switching topologies, respectively. (c) 2020 Elsevier B.V. All rights reserved.