Descriptor systems state-space conditions to guarantee negative imaginary properties without minimality restrictions

This paper is concerned with negative imaginary lemmas for descriptor systems. Without the minimal state-space realization assumption, sufficient conditions are developed for a negative imaginary lemma and a strictly negative imaginary lemma, respectively. As corollaries, sufficient conditions are derived to ensure the systems are both admissible and negative imaginary. Also, new sufficient negative imaginary lemmas are found for standard linear systems as special cases. The developed negative imaginary lemmas are applicable to descriptor systems with impulse modes. Two examples are used to illustrate the theory.