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Titolo: Numerical computation of the minimal Hinfinity norm of the discretetime output feedback control problem
Autore: Lin, WW; Wang, CS; Xu, QF;
 Indirizzi:
 Natl Tsing Hua Univ, Dept Math, Hsinchu, Taiwan Natl Tsing Hua Univ Hsinchu Taiwan Hua Univ, Dept Math, Hsinchu, Taiwan
 Titolo Testata:
 SIAM JOURNAL ON NUMERICAL ANALYSIS
fascicolo: 2,
volume: 38,
anno: 2000,
pagine: 515  547
 SICI:
 00361429(20000810)38:2<515:NCOTMH>2.0.ZU;2G
 Fonte:
 ISI
 Lingua:
 ENG
 Soggetto:
 RICCATIEQUATIONS; ALGORITHM; MATRIX;
 Keywords:
 discretetime; Hinfinity control; output feedback; optimal Hinfinity norm; symplectic; deflating subspace; singular pencil;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Physical, Chemical & Earth Sciences
 Citazioni:
 24
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Lin, WW Natl Tsing Hua Univ, Dept Math, Hsinchu, Taiwan Natl Tsing Hua Univ Hsinchu Taiwan , Dept Math, Hsinchu, Taiwan



 Citazione:
 W.W. Lin et al., "Numerical computation of the minimal Hinfinity norm of the discretetime output feedback control problem", SIAM J NUM, 38(2), 2000, pp. 515547
Abstract
Numerical computation of the minimal Hinfinity norm for the discretetimeoutput feedback control problem is considered. First of all, a lower boundis established in terms of the Hinfinity norm of certain stable transfer functions. Since the computational work in the evaluation of the Hinfinitynorm of a stable transfer function involves the determination of unimodular eigenvalues of the associated parameterized symplectic pencil of matrices, we discuss in detail how to get a numerically reliable solution when the pencil becomes singular as the parameter varies. Next, by exploiting the stable deflating subspaces of the two parameterized symplectic pencils derived by Iglesias and Glover in 1991, we characterize the critical points such that the corresponding two discretetime Riccati equations ( with parameterr) have stabilizing positive semidefinite solutions and satisfy certain inertia conditions. This characterization makes some kind of secant method applicable for finding these critical points. Finally, using the maximum of the two critical points as the starting point, we then devise an algorithm for computing the optimal ( minimal) Hinfinity norm by considering a secantmethod applied to the spectral radius (function of r) of the product of the corresponding two Riccati solutions. Numerical aspects are addressed throughout. In addition, some algebraic verifiable examples are given.
ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 18/11/18 alle ore 05:35:26