Robust feedback stability of negative imaginary systems: An integral quadratic constraint approach

Sufficient conditions for stability of feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. These extend existing results in the literature by exploiting the flexibility present at the static and infinite frequencies to reduce conservatism. Negative imaginary transfer functions with poles on the imaginary axis are accommodated using a recently generalised IQC-based robustness result. In particular, the negative imaginary property of systems is shown to give rise to IQCs on positive frequencies that are bounded away from zero and infinity. Additional quadratic conditions are introduced to take care of the IQCs near the DC and instantaneous gains of the systems.