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Singular perturbation margin and generalised gain margin for nonlinear time-invariant systems

Singular perturbation margin and generalised gain margin for nonlinear time-invariant systems In this paper, singular perturbation margin (SPM) and generalised gain margin (GGM) are proposed as the classical phase margin and gain margin like stability metrics for nonlinear systems established from the view of the singular perturbation and the regular perturbation, respectively. The problem of SPM and GGM assessment of a nonlinear nominal system is formulated. The SPM and GGM formulations are provided as the functions of radius of attraction (ROA), which is introduced as a conservative measure of the domain of attraction (DOA). Furthermore, the ROA constrained SPM and GGM analysis are processed through two stages: (1) the SPM and GGM assessment for nonlinear systems at the equilibrium point, based on the SPM and GGM equilibrium theorems, including time-invariant and time-varying cases (Theorem 5.3, Theorem 5.2, Theorem 5.4 and Theorem 5.5); (2) the establishment of the relationship between the SPM or GGM and the ROA for nonlinear time-invariant systems through the construction of the Lyapunov function for the singularly perturbed model (Theorem 6.1 and Section 6.2.3). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Control Taylor & Francis

Singular perturbation margin and generalised gain margin for nonlinear time-invariant systems

International Journal of Control , Volume 89 (3): 18 – Mar 3, 2016
18 pages

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References (33)

Publisher
Taylor & Francis
Copyright
© 2015 Taylor & Francis
ISSN
1366-5820
eISSN
0020-7179
DOI
10.1080/00207179.2015.1079738
Publisher site
See Article on Publisher Site

Abstract

In this paper, singular perturbation margin (SPM) and generalised gain margin (GGM) are proposed as the classical phase margin and gain margin like stability metrics for nonlinear systems established from the view of the singular perturbation and the regular perturbation, respectively. The problem of SPM and GGM assessment of a nonlinear nominal system is formulated. The SPM and GGM formulations are provided as the functions of radius of attraction (ROA), which is introduced as a conservative measure of the domain of attraction (DOA). Furthermore, the ROA constrained SPM and GGM analysis are processed through two stages: (1) the SPM and GGM assessment for nonlinear systems at the equilibrium point, based on the SPM and GGM equilibrium theorems, including time-invariant and time-varying cases (Theorem 5.3, Theorem 5.2, Theorem 5.4 and Theorem 5.5); (2) the establishment of the relationship between the SPM or GGM and the ROA for nonlinear time-invariant systems through the construction of the Lyapunov function for the singularly perturbed model (Theorem 6.1 and Section 6.2.3).

Journal

International Journal of ControlTaylor & Francis

Published: Mar 3, 2016

Keywords: singular perturbation; regular perturbation; stability metrics; nonlinear time-invariant systems

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