Group pinning consensus under fixed and randomly switching topologies with acyclic partition

This paper addresses group consensus problems in generic linearmulti-agent systems with directed information flow over (i) fixedtopology and (ii) randomly switching topology governed by acontinuous-time homogeneous Markov process. We propose two types ofpinning control protocols to ensure group consensus regardless ofthe magnitude of the coupling strengths among the agents. In thecase of randomly switching topology, we show that the groupconsensus behavior is unrelated to the magnitude of the couplingsamong agents if the union of the topologies corresponding to thepositive recurrent states of the Markov process possesses an acyclicpartition. Sufficient conditions for achieving group consensus arepresented in terms of simple graphic conditions, which are easy tobe checked compared to conventional algebraic criteria. Simulationexamples are also presented to validate the effectiveness of thetheoretical results.