4.1 Article

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

期刊

IEEE CONTROL SYSTEMS LETTERS
卷 6, 期 -, 页码 403-408

出版社

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LCSYS.2021.3077862

关键词

Numerical stability; Stability criteria; Poles and zeros; Filtering theory; Asymptotic stability; Frequency response; Feedback loop; Negative imaginary system; positive feedback; DC loop gain; internal stability

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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.
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.

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