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

TL;DR

This paper establishes conditions under which large-scale switched networks with QSR-dissipative agents maintain L2 stability, simplifying analysis by using a common storage function across all modes, applicable to systems like swarm drones.

Contribution

It links QSR-dissipativity with L2 stability in switched networks and introduces a method to ensure stability using a common storage function, reducing computational complexity.

Findings

Derived conditions for L2 stability in switched networks.

Established a common storage function for all switching modes.

Demonstrated stability analysis on swarm drone networks.

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.