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Generalized ℋ︁ 2 model approximation for differential linear repetitive processes
Author(s) -
Wu Ligang,
Zheng Wei Xing,
Su Xiaojie
Publication year - 2011
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.930
Subject(s) - linearization , mathematics , approximation error , convex optimization , linear approximation , projection (relational algebra) , scalar (mathematics) , linear matrix inequality , regular polygon , mathematical optimization , nonlinear system , algorithm , physics , geometry , quantum mechanics
This paper investigates the generalized ℋ 2 model approximation for differential linear repetitive processes (LRPs). For a given LRP, which is assumed to be stable along the pass, we are aimed at constructing a reduced‐order model of the LRP such that the generalized ℋ 2 gain of the approximation error LRP between the original LRP and the reduced‐order one is less than a prescribed scalar. A sufficient condition to characterize the bound of the generalized ℋ 2 gain of the approximation error LRP is presented in terms of linear matrix inequalities (LMIs). Two different approaches are proposed to solve the considered generalized ℋ 2 model approximation problem. One is the convex linearization approach, which casts the model approximation into a convex optimization problem, while the other is the projection approach, which casts the model approximation into a sequential minimization problem subject to LMI constraints by employing the cone complementary linearization algorithm. A numerical example is provided to demonstrate the proposed theories. Copyright © 2010 John Wiley & Sons, Ltd.