Abstract
This paper studies the stability of the feedback interconnection of discrete-time negative imaginary (D-NI) systems through integral quadratic constraints (IQCs). Applying the latest IQC-based result to the D-NI systems with poles on the unit circle, a necessary and sufficient condition for the stability of the feedback interconnection of a D-NI system without poles at and a strictly negative imaginary (D-SNI) system is developed. The stability of the feedback interconnection of a D-NI system with poles at 1 and a D-SNI system is also studied. Moreover, a sufficient condition for the internal stability of the interconnection of unstable D-NI systems is obtained. Three examples are given to illustrate that the main results are broader than some early results.
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