Negative Imaginary Stability Result Allowing Purely Imaginary Poles in Both the Interconnected Systems

This letter extends the class of systems to which negative imaginary (NI) stability result can be (directly) applied. The existing closed-loop stability results for NI interconnections require at least one of the systems to satisfy strictly negative imaginary (SNI) properties and hence do not allow purely imaginary poles in both the systems. In contrast to this, a set of necessary and sufficient conditions is derived in this brief for the internal stability of two NI systems in a positive feedback loop with possible poles on the imaginary axis excluding the origin. This proposed result also captures all the existing closed-loop stability results of NI systems, without poles at the origin, as special cases. Illustrative numerical examples are studied to show the usefulness of this development.

Automated summary

This paper presents a new approach for applying negative imaginary (NI) stability results to a wider range of systems. This approach no longer requires the existence of strictly negative imaginary (SNI) properties in the systems and can handle systems with purely imaginary poles. Additionally, this approach can cover existing stability results of NI systems.