Robust Stability of Time-varying Polytopic Systems by the Attractive Ellipsoid Method

Garcia, P. and Ampountolas, K. (2019) Robust Stability of Time-varying Polytopic Systems by the Attractive Ellipsoid Method. In: 2019 American Control Conference (ACC), Philadelphia, PA, USA, 10-12 Jul 2019, pp. 1139-1144. ISBN 9781538679265 (doi: 10.23919/ACC.2019.8814432)

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Abstract

This paper concerns the robust stabilization of continuous-time polytopic systems subject to unknown but bounded perturbations. To tackle this problem, the attractive ellipsoid method (AEM) is employed. The AEM aims to determine an asymptotically attractive (invariant) ellipsoid such that the state trajectories of the system converge to a small neighborhood of the origin despite the presence of nonvanishing perturbations. An alternative form of the elimination lemma is used to derive new LMI conditions, where the state-space matrices are decoupled from the stabilizing Lyapunov matrix. Then a robust state-feedback control law is obtained by semi-definite convex optimization, which is numerically tractable. Further, the gain-scheduled state-feedback control problem is considered within the AEM framework. Numerical examples are given to illustrate the proposed AEM and its improvements over previous works. Precisely, it is demonstrated that the minimal size ellipsoids obtained by the proposed AEM are smaller compared to previous works, and thus the proposed control design is less conservative.

Item Type:Conference Proceedings
Keywords:Continuous time systems, control system synthesis, convex programming, state feedback, linear matrix inequalities, linear systems, Lyapunov matrix equations, robust control, time-varying systems, uncertain systems.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ampountolas, Dr Konstantinos
Authors: Garcia, P., and Ampountolas, K.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
ISSN:2378-5861
ISBN:9781538679265
Published Online:29 August 2019
Copyright Holders:Copyright © 2019 AACC
First Published:First published in 2019 American Control Conference (ACC): 1139-1144
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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