Sufficient and necessary conditions for the stability of positive feedback
interconnections of negative imaginary systems are derived via an integral
quadratic constraint (IQC) approach. The IQC framework accommodates
distributed-parameter systems with irrational transfer function
representations, while generalising existing results in the literature and
allowing exploitation of flexibility at zero and infinite frequencies to reduce
conservatism in the analysis. The main results manifest the important property
that the negative imaginariness of systems gives rise to a certain form of IQCs
on positive frequencies that are bounded away from zero and infinity. Two
additional sets of IQCs on the DC and instantaneous gains of the systems are
shown to be sufficient and necessary for closed-loop stability along a homotopy
of systems.Comment: Submitted to Automatica, A preliminary version of this paper appeared
in the Proceedings of the 2015 European Control Conferenc
