The generalised singular perturbation approximation for bounded real and positive real control systems

Guiver, Christopher

Abstract

The generalised singular perturbation approximation (GSPA) is considered as a model reduction scheme for bounded real and positive real linear control systems. The GSPA is a state-space approach to truncation with the defining property that the transfer function of the approximation interpolates the original transfer function at a prescribed point in the closed right half complex plane. Both familiar balanced truncation and singular perturbation approximation are known to be special cases of the GSPA, interpolating at infinity and at zero, respectively. Suitably modified, we show that the GSPA preserves classical dissipativity properties of the truncations, and existing a priori error bounds for these balanced truncation schemes are satisfied as well.

Citation

Guiver, C. (2019). The generalised singular perturbation approximation for bounded real and positive real control systems. Mathematical Control and Related Fields, 9(2), 313-350. https://doi.org/10.3934/mcrf.2019016

• Journal Article Type: Article
• Acceptance Date: Aug 19, 2018
• Publication Date: 2019-06
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Jul 24, 2020
• Journal: Mathematical Control and Related Fields
• Print ISSN: 2156-8472
• Publisher: American Institute of Mathematical Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 2
• Pages: 313-350
• DOI: https://doi.org/10.3934/mcrf.2019016
• Keywords: Balanced truncation, Dissipative system, Linear system, Model reduction, Rational interpolation, Singular perturbation approximation
• Public URL: http://researchrepository.napier.ac.uk/Output/2677272