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Gain‐scheduled dynamic output feedback control for discrete‐time LPV systems
Author(s) -
De Caigny J.,
Camino J. F.,
Oliveira R. C. L. F.,
Peres P. L. D.,
Swevers J.
Publication year - 2012
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.1711
Subject(s) - control theory (sociology) , discrete time and continuous time , gain scheduling , lyapunov function , output feedback , scheduling (production processes) , computer science , mathematical optimization , mathematics , linear matrix inequality , control (management) , nonlinear system , statistics , physics , quantum mechanics , artificial intelligence
SUMMARY This paper presents synthesis conditions for the design of gain‐scheduled dynamic output feedback controllers for discrete‐time linear parameter‐varying systems. The state‐space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter. As an immediate extension, conditions for the synthesis of a multiobjective ℋ ∞ and ℋ 2 gain‐scheduled dynamic feedback controller are also provided. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real‐time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter‐dependent Lyapunov function. An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.