Dissipativity and L2 Stability of Large-Scale Networks with Changing Interconnections

Abstract: In this paper, the L2 stability of switched networks is studied based on the QSR-dissipativity of each agent. While the integration of dissipativity with switched systems has received considerable attention, most previous studies have focused on passivity, internal stability, or feedback networks involving only two agents. This work makes two contributions: first, the relationship between switched QSR-dissipativity and L2 stability is established based on the properties of dissipativity parameters of switched systems; and second, conditions for L2 stability of networks consisting of QSR-dissipative agents with switching interconnection topologies are derived. Crucially, this shows that a common storage function will exist across all modes, avoiding the need to find one, which becomes computationally taxing for large networks with many possible configurations. Numerical examples demonstrate how this can facilitate stability analysis for networked systems under arbitrary switching of swarm drones.