Finite frequency negative imaginary lemmas for descriptor systems

摘要

This paper studies the finite frequency negative imaginary properties of descriptor systems in terms of state-space realization. Necessary and sufficient conditions are provided for descriptor systems satisfying finite frequency negative imaginary properties based on linear matrix inequalities with equality constraints. Also, a time-domain interpretation of the finite frequency negative imaginary properties for descriptor systems is provided in term of the systems input, output, state. Finally, an example is used to illustrate the result.