Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems
For control theorists and engineers, this provides a more general and less conservative stability analysis framework for distributed-parameter negative imaginary systems.
The paper derives sufficient and necessary conditions for stability of positive feedback interconnections of negative imaginary systems using an IQC approach, generalizing existing results and reducing conservatism by exploiting flexibility at zero and infinite frequencies.
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.