PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2001 | 11 | 6 | 1331-1360
Tytuł artykułu

Time-variant Darlington synthesis and induced realizations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a block lower triangular contraction T, necessary and sufficient conditions are given in order that there exist block lower triangular contractions T_{1,1}, T_{2,1} and T_{2,2} such that T_{1,1} T U_T = [ ] T_{2,1} T_{2,2} is unitary. For the case when T^*_{1,1} and T_{2,2} have dense ranges, all such embeddings are described. Each unitary embedding of UT induces a contractive realization of T , and various properties of this realization are characterized in terms of the unitary embedding.
Rocznik
Tom
11
Numer
6
Strony
1331-1360
Opis fizyczny
Daty
wydano
2001
Twórcy
autor
  • Division of Mathematics and Computer Sciences, Faculty of Sciences, De Boelelaan 1081 a, 1081 HV Amsterdam, The Netherlands
Bibliografia
  • Arov D.Z. (1971): Darlington’s method for dissipative systems. — Dokl. Akad. Nauk SSSR, Vol.201, No.3, pp.559–562; English translation: Soviet Physics Doklady, Vol.16, No.11, pp.954–956.
  • Arov D.Z. (1979): Stable dissipative linear stationary dynamical scattering systems. — J. Oper. Theory, Vol.2, No.1, pp.95–126 (in Russian).
  • Arov D.Z. (1985): Linear stationary passive systems with losses. — 2-nd doctoral dissertation, Phys. Math. Sci., Institute of Mathematics, Akad. Nauk Ukr. SSR, Kiev.
  • Arov D.Z., Kaashoek M.A. and Pik D.R. (1998): Optimal time-variant systems and factorization of operators, I: Minimal and optimal systems. — Int. Eqns. Oper. Theory, Vol.31, No.4, pp.389–420.
  • Arov D.Z., Kaashoek M.A. and Pik D.R. (2000): Optimal time variant systems and factorization of operators, II: Factorization. — J. Oper. Theory, Vol.43, No.2, pp.263–294.
  • Belevitch V. (1968): Classical Network Theory. — San Francisco: Holden-Day.
  • Constantinescu T. (1995): Schur Parameters, Factorizations and Dilation Problems. — Basel: Birkhäuser.
  • Dewilde P. (1971): Roomy scattering matrix synthesis. — Tech. Rep., Dept. of Mathematics, Univ. of California, Berkeley.
  • Dewilde P. (1999): Generalized Darlington Synthesis. — IEEE Trans. Circ. Syst., 1: Fund. Theory Appl., Vol.46, No.1, pp.41–58.
  • Dewilde P. and Van der Veen A. (1998): Time-Varying Systems and Computations. — Boston: Kluwer Academic Publishers.
  • Douglas R.G. and William Helton J. (1973): Inner dilations of analytic matrix functions and Darlington synthesis. — Acta Sci. Math. (Szeged), Vol.34, pp.61–67. 1360
  • Douglas R.G., Shapiro A.L., and Shields A.L. (1970): Cyclic vectors and invariant subspaces for the backward shift. — Ann. Inst. Fourier (Grenoble), Vol.20, No.1, pp.37–76.
  • Foias C., Frazho A.E., Gohberg I. and Kaashoek, M.A. (1998); Metric Constrained Interpolation, Commutant Lifting and Systems. — Basel: Birkhäuser.
  • Gohberg I., Kaashoek M.A. and Lerer L. (1992): Minimality and realization of discrete time- variant systems, In: Time-variant Systems and Interpolation (I. Gohberg, Ed.). — Basel: Birkhäuser, pp.261–296.
  • Halanay A. and Ionescu V. (1994): Time-Varying Discrete Linear Systems, Input-Output Operators, Riccati Equations, Disturbance Attenuation. — Basel: Birkhäuser.
  • Kaashoek M.A. and Pik D.R. (1998): Factorization of lower triangular unitary operators with finite Kronecker index into elementary factors, In: Recent Progress in Operator Theory, International Workshop on Operator Theory and Applications, IWOTA 95, Regensburg, Germany, July 31–August 4, 1995 (I. Gohberg, R. Mennicken, C. Tretter, Eds.). — Basel: Birkhäuser, pp.183–217.
  • Pik D.R. (1999): Block lower triangular operators and optimal contractive systems. — Ph.D. Thesis, Vrije Universiteit Amsterdam, Amsterdam.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv11i6p1331bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.