Frequency-Limited Model Reduction for Linear Positive Systems: A Successive Optimization Method

This paper studies frequency-limited model reduction for linear positive systems. Specifically, the objective is to develop a reduced-order model for a high-order positive system that preserves the positivity, while minimizing the approximation error within a given H∞ upper bound over a limited freq...

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Bibliographic Details
Published inApplied sciences Vol. 13; no. 6; p. 4039
Main Authors Ren, Yingying, Wang, Qian
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2023
Subjects
Algorithms
Analysis
Approximation
bilinear matrix inequalities
Control theory
Convex analysis
frequency-limited model reduction
Methods
Optimization
positive systems
successive convex optimization algorithm
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Summary:This paper studies frequency-limited model reduction for linear positive systems. Specifically, the objective is to develop a reduced-order model for a high-order positive system that preserves the positivity, while minimizing the approximation error within a given H∞ upper bound over a limited frequency interval. To characterize the finite-frequency H∞ specification and stability, we first present the analysis conditions in the form of bilinear matrix inequalities. By leveraging these conditions, we derive convex surrogate constraints by means of an inner-approximation strategy. Based on this, we construct a novel iterative algorithm for calculating and optimizing the reduced-order model. Finally, the effectiveness of the proposed model reduction method is illustrated with a numerical example.
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ISSN:2076-3417
2076-3417
DOI:10.3390/app13064039