Sampled-time containment control of high-order continuous-time MASs under heterogenuous time-varying delays and switching topologies: A scrambling matrix approach

Abstract

This paper studies the containment control problem for high-order continuous-time multi-agent systems (MASs) under switching topologies and time-varying delays. We propose a distributed sampled-time containment protocol in which the restriction of choosing weights of the communication links from a finite set is eliminated. Under such a protocol, the states of the followers will asymptotically converge to the convex hull spanned by those of the leaders. Based on the properties of scrambling matrices, necessary and sufficient containment criteria are obtained for the network of agents with arbitrary bounded communication delays and switching interaction topologies. The proposed condition does not need the communication graph has a united spanning tree at each time instant and only requires that the union of communication graphs has a united spanning tree over a bounded period of time. In addition, the appropriate feedback gains are computed via given mathematical relations. Some numerical examples are given to demonstrate the effectiveness of the new protocols.