Robust performance analysis for uncertain negative‐imaginary systems |
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Authors: | Zhuoyue Song Alexander Lanzon Sourav Patra Ian R. Petersen |
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Affiliation: | 1. Control Systems Centre, School of Electrical and Electronic Engineering, University of Manchester, Manchester M60 1QD, U.K.;2. School of Information Technology and Electrical Engineering, University of New South Wales at the Australian Defence Force Academy, Canberra ACT 2006, Australia |
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Abstract: | Negative‐imaginary systems are important in engineering practice as this class of systems appears quite often in practical problems, for example, lightly damped flexible structures with collocated position sensors and force actuators. In this paper, an analytical framework for robust performance of uncertain negative‐imaginary systems is proposed. The results are obtained by transforming negative‐imaginary systems into a bounded‐real framework via the positive‐real property. This paper deals with all the significant technical difficulties that appear due to the transformation and the punctured j ω‐axis frequency condition of negative‐imaginary systems. The problem is equivalently cast into a structured singular value condition that gives a quantitative performance test for this class of systems. This result also gives an analytical framework for robust stability when the perturbations are mixture of bounded‐real and negative‐imaginary uncertainties. A numerical example is presented to show the usefulness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | negative‐imaginary systems bounded‐real positive‐real lightly damped systems ℋ ︁ ∞ control structured singular value robust performance |
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