Solvability of a consensus problem for multiagent systems (MASs) in switching networks heavily relies on stablization techniques for switched systems. The consensus problem becomes challenging when the agent dynamics are complicated that requires stability of a switched system composed of unstable subsystems. Moreover, complicated dynamics bring other coupling structures into a switched system. To solve the consensus problem in such a scenario, we study the input-to-state stability property of a switched system with external influence and hence design a stablization controller for a switched system of interconnected components using the small gain theorem. The controller successfully leads to the solution to the consensus problem for a class of nonlinear, heterogeneous, and uncertain MASs in switching networks with jointly connected topology.