A test for stability robustness of linear time‐varying systems utilizing the linear time‐invariant ν‐gap metric |
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Authors: | Wynita M Griggs Alexander Lanzon Brian D O Anderson |
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Affiliation: | 1. Department of Information Engineering, Research School of Information Sciences and Engineering, The Australian National University, Canberra, ACT 0200, Australia;2. Control Systems Centre, School of Electrical and Electronic Engineering, University of Manchester, Sackville Street, Manchester M60 1QD, U.K.;3. National ICT Australia Limited, Locked Bag 8001, Canberra, ACT 2601, Australia |
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Abstract: | A stability robustness test is developed for internally stable, nominal, linear time‐invariant (LTI) feedback systems subject to structured, linear time‐varying uncertainty. There exists (in the literature) a necessary and sufficient structured small gain condition that determines robust stability in such cases. In this paper, the structured small gain theorem is utilized to formulate a (sufficient) stability robustness condition in a scaled LTI ν‐gap metric framework. The scaled LTI ν‐gap metric stability condition is shown to be computable via linear matrix inequality techniques, similar to the structured small gain condition. Apart from a comparison with a generalized robust stability margin as the final part of the stability test, however, the solution algorithm implemented to test the scaled LTI ν‐gap metric stability robustness condition is shown to be independent of knowledge about the controller transfer function (as opposed to the LMI feasibility problem associated with the scaled small gain condition which is dependent on knowledge about the controller). Thus, given a nominal plant and a structured uncertainty set, the stability robustness condition presented in this paper provides a single constraint on a controller (in terms of a large enough generalized robust stability margin) that (sufficiently) guarantees to stabilize all plants in the uncertainty set. Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | ν ‐gap metric stability robustness structured uncertainty linear time‐varying uncertainty |
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