Primal and dual stability critera applied to large interconnected systems
Abstract:
Primal and dual formulations of stability criteria based on integral quadratic constraints (IQC) are discussed in this paper. The foundation for IQC based stability analysis is to use a convex cone of multipliers to characterize the uncertainty in a system. The primal and dual stability criteria are formulated as convex feasibility tests involving the nominal dynamics and multipliers from the cone and the polar cone, respectively. The motivation for introducing the dual is that it provides additional insight into the stability criterion and is sometimes easier to use than the primal. In this paper we consider the case when the uncertainty represents the interconnection of a complex network such as the Internet or a heterogeneous consensus network. The multipliers are used to describe characteristic properties of the network such as the spectral location or the bi-partite structure of the graph in Internet congestion control. We show that the dual criterion sometimes reveals structural properties of the interconnection which are easy to investigate using low dimensional graphical tests.