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Titolo:
Numerical computation of the minimal H-infinity norm of the discrete-time 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:
0036-1429(20000810)38:2<515:NCOTMH>2.0.ZU;2-G
Fonte:
ISI
Lingua:
ENG
Soggetto:
RICCATI-EQUATIONS; ALGORITHM; MATRIX;
Keywords:
discrete-time; H-infinity control; output feedback; optimal H-infinity 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 H-infinity norm of the discrete-time output feedback control problem", SIAM J NUM, 38(2), 2000, pp. 515-547

Abstract

Numerical computation of the minimal H-infinity norm for the discrete-timeoutput feedback control problem is considered. First of all, a lower boundis established in terms of the H-infinity norm of certain stable transfer functions. Since the computational work in the evaluation of the H-infinitynorm 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 discrete-time 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) H-infinity 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.

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Documento generato il 19/07/18 alle ore 13:19:07