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Pre‐filtering and post‐filtering in gain‐scheduled output‐feedback H ∞ control
Author(s) -
Sehr Martin A.,
de Oliveira Maurício C.
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3738
Subject(s) - control theory (sociology) , controller (irrigation) , linear matrix inequality , output feedback , state (computer science) , computer science , control (management) , quadratic equation , full state feedback , mathematical optimization , mathematics , algorithm , artificial intelligence , geometry , agronomy , biology
Summary Linear matrix inequality (LMI) design conditions for gain‐scheduled output‐feedbackH ∞control rely on assumptions constraining either system or controller matrices. Throughout the literature, it is common practice to avoid imposing restrictive assumptions on the controller, which may appear undesirable, in favor of state augmentations via pre‐filtering and post‐filtering to construct auxiliary augmented systems that comply with the alternative assumptions on the system matrices. This technique brings in the additional cost of increased state dimensions of the resulting gain‐scheduled output‐feedback controllers. In this paper, we explore the interplay and inherent trade‐offs between state augmentation, controller structure, and performance. We revisit LMI design conditions for quadratic output‐feedbackH ∞control and demonstrate that state augmentation via pre‐filtering and post‐filtering in order to avoid constraints on the controller matrices is never advantageous even without taking into account the added complexity and propensity for numerical issues associated with state augmentation. As an additional contribution, we extend this observation to recently introduced modified LMI conditions allowing combined – however less restrictive – assumptions on system and controller matrices. Copyright © 2016 John Wiley & Sons, Ltd.

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