Finite frequency negative imaginary systems

This paper is concerned with finite frequency negative imaginary (FFNI) systems. The paper introduces the concept of FFNI transfer function matrices, and the relationship between the FFNI property and the finite frequency positive real (FFPR) property of transfer function matrices is established. The paper also establishes an FFNI lemma which gives a necessary and sufficient condition on the 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 system input, output and state. An example is presented to illustrate the FFNI concept and the FFNI lemma.