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Factorization‐based frequency‐weighted optimal Hankel‐norm model reduction
Author(s) -
Kumar Deepak,
Sreeram Victor
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2096
Subject(s) - factorization , mathematics , norm (philosophy) , dixon's factorization method , algorithm , reduction (mathematics) , matrix decomposition , incomplete lu factorization , lti system theory , invariant (physics) , linear system , mathematical optimization , factorization of polynomials , mathematical analysis , eigenvalues and eigenvectors , physics , geometry , matrix polynomial , quantum mechanics , political science , polynomial , law , mathematical physics
In this paper, we present frequency‐weighted optimal Hankel‐norm model reduction algorithms for linear time‐invariant continuous‐time systems by representing an original higher‐order system into new fictitious systems. The new system representations are derived through factorization of the resulting sub‐matrices that are obtained after transformations. As the proposed approaches are factorization dependent, additional results with both approaches are included using another factorization of the fictitious input–output and weight matrices. The proposed algorithms generate stable reduced models with double‐sided weights and provide a substantial improvement in the weighted error. A numerical example is given to compare the efficacy of the proposed algorithms with the well‐known frequency‐weighted techniques.