Abstract
Systems with counterclockwise input–output dynamics (or negative imaginary transfer functions) arise in various applications such as the modeling of flexible mechanical structures or electrical circuits when certain kinds of measurements are taken. In this paper we introduce descriptor systems with such an additional structure. We state various of their properties and prove algebraic characterizations of negative imaginariness in terms of spectral conditions of certain structured matrix pencils. For this purpose we also analyze particular boundary cases which are characterized by properties of a structured Kronecker canonical form. Finally, we describe a method which can be used to restore the negative imaginary property in case that it is lost. This happens, e.g., when a system with theoretically negative imaginary transfer function is obtained by, e.g., model order reduction methods, linearization, or other approximations. The method is illustrated by numerical examples.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.