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Time-varying hierarchical multi-agent systems are common in manyapplications. A well-known solution to control these systems is to use statefeedback controllers that depend on the adjacency matrix to reach consensus.This solution has been applied so far to multi-agent systems with fixed ortime-varying communication topologies. In this paper, we considersingle-integrator multi-agent systems where only a subset of the agents areactive at any given time and the set of active agents is time-varying. Thistype of multi-agent system is relevant in applications such as modularmultilevel converters and water pumping systems. We develop a switchingalgorithm that periodically selects a set of active agents through a set ofgraphs that connect the follower agents with a leader agent. We further provethat the developed switching algorithm combined with a classic consensusprotocol yields convergence to a consensus state defined by the leader despitea time-varying set of active agents. The effectiveness of the switchingalgorithm is illustrated in two benchmark examples: a modular multilevelconverter and a water pumping system.

Consensus of hierarchical multi-agent systems with a time-varying set of active agents