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

TL;DR

The paper addresses stability in large-scale, switching-networked systems by linking QSR-dissipativity of individual agents to L2 stability under arbitrary switching. It derives conditions ensuring L2 stability for networks with switching interconnections and demonstrates that a common storage function exists across all modes, enabling distributed analysis without per-mode storage function design. The work highlights computational advantages over traditional dissipativity and Lyapunov approaches and supports its claims with numerical examples on swarm drones. Overall, it provides a scalable framework for stability analysis and controller synthesis in switched networks of many agents.

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.

Figures (1)

• Figure 2: System responses to L2 disturbances: The dotted lines indicate the switching instants. The right plot presents magnified views of the corresponding left plot.