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Title: Antiwindup for stable linear systems with input saturation: an LMI-based synthesis
Authors: Grimm, G.
Hatfield, J.
Postlethwaite, Ian
Teel, A. R.
Turner, Matthew C.
Zaccarian, L.
First Published: 2003
Citation: IEEE Transactions on Automatic Control, 2003, 48 (9), pp.1509-1525
Abstract: This paper considers closed-loop quadratic stability and L2 performance properties of linear control systems subject to input saturation. More specifically, these properties are examined within the context of the popular linear antiwindup augmentation paradigm. Linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification, called the "unconstrained closed-loop behavior." Building on known results on H∞ and LPV synthesis, the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem, which has an attractive system theoretic interpretation: the lower bound on the achievable L2 performance is the maximum of the open and unconstrained closed-loop L2 gains. In the special cases of zero-order (static) and plant-order antiwindup compensation, the feasibility conditions become (convex) linear matrix inequalities. It is shown that, if (and only if) the plant is asymptotically stable, plant-order linear antiwindup compensation is always feasible for large enough L2 gain and that static antiwindup compensation is feasible provided a quasi-common Lyapunov function, between the open-loop and unconstrained closed-loop, exists. Using the solutions to the matrix feasibility problems, the synthesis of the antiwindup augmentation achieving the desired level of L2 performance is then accomplished by solving an additional LMI.
DOI Link: 10.1109/TAC.2003.816965
ISSN: 0018-9286
Type: Article
Rights: Copyright © 2003 IEEE. Reprinted from IEEE Transactions on Automatic Control, 2003, 48 (9), pp.1509-1525. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Leicester’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
This paper was published as IEEE Transactions on Automatic Control, 2003, 48 (9), pp.1509-1525. It is also available from DOI: 10.1109/TAC.2003.816965
Appears in Collections:Published Articles, Dept. of Engineering

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