Externally positive linear systems from transfer function properties

Abstract

The characterisation of single-input-single-output externally positive linear systems is considered. A complete characterisation of the class of externally positive second-order and a class of underdamped third-order systems is given and connections to negative-imaginary systems are highlighted. It is shown that negative-imaginary systems have non-negative step responses, leading to a condition for external positivity based on negative imaginary systems theory. Finally, a class of externally positive systems which can be verified using the developed results but which fail a recently developed numerical test for external positivity based upon linear matrix inequalities are introduced. These results extend the class of system for which external positivity can be verified, facilitating large-scale control and less conservative absolute stability analysis.

Metadata

Authors/Creators:

Drummond, R. https://orcid.org/0000-0002-2586-1718
Turner, M.C. https://orcid.org/0000-0003-2161-7635

© 2023 The Authors. Except as otherwise noted, this author-accepted version of a journal article published in IEEE Control Systems Letters is made available via the University of Sheffield Research Publications and Copyright Policy under the terms of the Creative Commons Attribution 4.0 International License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/

Keywords:

Control Engineering, Mechatronics and Robotics; Engineering

Dates: