Finite Frequency Negative Imaginary Systems

This technical note is concerned with finite frequency negative imaginary (FFNI) systems. Firstly, the concept of FFNI transfer function matrices is introduced, and the relationship between the FFNI property and the finite frequency positive real property of transfer function matrices is studied. Then the technical note establishes an FFNI lemma which gives a necessary and sufficient condition on matrices appearing in a minimal state-space realization for a transfer function to be FFNI. Also, a time-domain interpretation of the FFNI property is provided in terms of the system input, output and state. Finally, an example is presented to illustrate the FFNI concept and the FFNI lemma.