Continuous time LTI systems under lossless positive real transformations: open-loop balanced representation and truncated reduced-order models. Issue 7 (3rd July 2017)

• Record Type: Journal Article
• Authors: Buscarino, A.; Fortuna, L.; Frasca, M.; Xibilia, M. G.
• Is Part Of: International journal of control. Volume 90:Issue 7(2017)
• Page Start: 1437
• Page End: 1445
• Publication Date: 2017-07-03
• Subjects: Continuous time LTI systems -- model order reduction -- open-loop balanced realisation -- lossless positive real transformation; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2016.1208368
• Languages: English
• ISSNs: 0020-7179

Abstract

ABSTRACT: In this paper, new results on the open-loop balanced representation of continuous time linear time-invariant systems are reported. More particularly, the effect of lossless positive real transformations on open-loop balanced representations is investigated with specific attention to the problem of model order reduction. The properties of systems where a lossless positive real transformation has been applied are discussed showing that, if the original system is open-loop balanced, the resulting transformed system is still open-loop balanced. Furthermore, the singular values of the transformed system are related to those of the original one. These results allow to derive a model order reduction strategy for this class of systems that leads to a consistent decrease of the numerical complexity. The proposed approach reveals to be of particular interest for the design of reduced-order systems with specific amplitude responses, including analog multiband filters.