Interval frequency negative imaginary systems

Junlin Xiong and Shengyu Zhai

International Journal of Systems Science, 2018, vol. 49, issue 14, 2968-2980

Abstract: This paper studies interval frequency negative imaginary (IFNI) systems based on minimal state-space realisations. Firstly, the concept of the IFNI transfer functions is introduced, and the relationship between the IFNI transfer functions and the interval frequency positive real transfer functions is established. Secondly, based on the generalised KYP lemma, a necessary and sufficient condition is derived for IFNI transfer functions with minimal state-space realisation in terms of linear matrix inequalities. Our results coincide with the existing negative imaginary lemma when the interval frequency set becomes the positive frequency set. Also, a time domain interpretation of the IFNI property is provided in terms of the system input, output and state. Finally, two examples are used to illustrate the developed theory.

Date: 2018
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DOI: 10.1080/00207721.2018.1529256

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