Primal and dual criteria for robust stability and their application to systems interconnected over a bipartite graph

A dual formulation of a standard stability criterion from robust control is derived and investigated. The dual provides additional insight into the stability criterion and is sometimes easier to use than the primal. This is illustrated for a class of systems interconnected over a bipartite graph. The dual criterion reveals structural properties of the interconnection which in some cases are easy to investigate using low complexity tests.