On state-space characterization for strict negative-imaginariness of LTI systems

Negative-imaginary systems appear quite often in engineering applications, for example, in flexible structures with collocated position sensors and force actuators, in electrical circuits, in system biology, etc. In this paper, a strongly strict negative-imaginary lemma is proposed to ensure the strict negative-imaginary property of an LTI system. This result will facilitate both robustness analysis and controller synthesis for interconnected negative-imaginary systems. In the proposed characterization, numerical advantages are achieved by avoiding a minimality assumption, a non-convex rank constraint and a non-strict inequality condition present in previous literature. Two numerical examples are provided to illustrate the effectiveness of the proposed results.