In this paper, the stability problem of a class of multi-agent tracking systems with quasi-cyclic switching topologies is investigated. The existing results of systems with switching topologies are usually achieved based on the assumption that the piecewise constant communication topologies are connected and the switchings are cyclic. The communication topologies are possible to be unconnected and it is difficult to guarantee the topologies switch circularly. The piecewise unconnected topology

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... akes the interactive multi-agent tracking system to be an unstable subsystem over this time interval. In order to relax the assumption constraint, a quasi-cyclic method is proposed, which allows the topologies of multi-agent systems to switch in a less conservative way. Moreover, the stability of the tracking system with the existence of unstable subsystems is analyzed based on switched control theory. It is obtained that the convergence rate is affected by the maximum dwell time of unstable subsystems. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.