Wiener-Hopf factorization of transfer functions of extended Pritchard-Salamon realizations

Mathematische Nachrichten

Volumn 196, Issue , 1998, Pages 71-102

  Kaashoek, M A ^a   Van Der Mee, C V M ^b   Ran, A C M ^a  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

Lyapunov equations; Pritchard salamon systems; Riccati equations; Transfer functions; Wiener hopf factorization

Indexed keywords

EID: 0032414872     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/mana.19981960105     Document Type: Article

References (25)

1. BALL, J. A., and CARPENTER, L.: Realizations of Products and Wiener-Hopf Factors for a Class of Matrix Functions Analytic in a Strip. In: KAASHOEK, M. A., VAN SCHUPPEN, J. H., and RAN, A. C. M. (Eds.), Signal Processing, Scattering and Operator Theory, Proceedings of the MTNS-89, Vol. III, pp. 291-299, Birkhäuser, Boston, 1990
2. BALL, J. A., and RAN, A. C. M.: Left Versus Right Canonical Wiener-Hopf Factorization. In: GOHBERG, I., and KAASHOEK, M. A., Constructive Methods of Wiener-Hopf Factorization, Birkhäuser OT 21, pp. 9-38, Basel and Boston, 1986
3. BART, H., GOHBERG, I., and KAASHOEK, M. A.: Minimal Factorization of Matrix and Operator Functions, Birkhäuser OT 1, Basel and Boston, 1979
4. BART, H., GOHBERG, I., and KAASHOEK, M. A.: Wiener-Hopf Factorization, Inverse Fourier Transforms and Exponentially Dichotomous Operators, J. Funct. Anal. 68 (1986), 1-42
5. BART, H., GOHBERG, I., and KAASHOEK, M. A.: Exponentially Dichotomous Operators and Inverse Fourier Transforms, Report 8511/M, Econometric Institute, Erasmus University of Rotterdam, The Netherlands, 1985
6. CURTAIN, R. F.: Equivalence of Input-Output Stability and Exponential Stability for Infinite-Dimensional Systems, Math. Systems Theory 21 (1988), 19-48
7. CURTAIN, R. F., LOGEMANN, H., TOWNLEY, S., and Zwart, H.: Well-Posedness, Stabilizability and Admissibility for Pritchard-Salamon Systems, J. Math. Systems, Estim. Control 4 (1994), 493-496
8. CURTAIN, R. F., and RAN, A. C. M.: Explicit Formulas for Hankel Norm Approximations of Infinite-Dimensional Systems. Integral Equations and Operator Theory 12 (1989), 455-469
9. CURTAIN, R. F., and ZWART, H.: An Introduction to Infinite-Dimensional Linear System Theory, Springer TAM 21, New York, etc., 1995
10. CURTAIN, R. F., and ZWART, H.: The Nehari Problem for the Pritchard-Salamon Class of Infinite Dimensional Linear Systems: A Direct Approach, Integral Equations and Operator Theory 18 (1994), 130-153
11. DIESTEL, J., and UHL, J. J., JR.: Vector Measures, Math. Surveys, Vol. 15, Amer. Math. Soc., Providence, R. I., 1977
12. ∞ Control, SIAM J. Control and Opt. 28 (1990), 1350-1371
13. GOHBERG, I., GOLDBERG, S., and KAASHOEK, M. A.: Classes of Linear Operators, Vol. I, Birkhäuser OT 49, Basel and Boston, 1990
14. GOHBERG, I. C., and LEITERER, J.: Factorization of Operator Functions with respect to a Contour. II. Canonical Factorization of Operators Close to the Identity, Math. Nachrichten 54 (1972), 41-74 [Russian]
15. GOHBERG, I., and RAN, A. C. M.: On Pseudo-Canonical Factorization of Rational Matrix Functions. Indagationes Mathematicae N. S. 4 (1993), 51-63
16. GOHBERG, I., AND RUBINSTEIN, S.: Proper Contractions and Their Unitary Minimal Completions. In: I. GOHBERG, Ed., Topics in Interpolation Theory of Rational Matrix-Valued Functions, OT 33, 109-122, Birkhäuser Verlag, Basel, 1988
17. GREENBERG, W., VAN DER MEE, C. V. M., and PROTOPOPESCU, V.: Boundary Value Problems in Abstract Kinetic Theory, Birkhäuser OT 23, Basel and Boston, 1987
18. HILLE, E., and PHILLIPS, R. S.: Functional Analysis, and Semigroups, Amer. Math. Soc., Providence, R. I., 1957
19. KAASHOEK, M. A., VAN DER MEE, C.V. M., and RAN, A. C. M.: Weighting Operator Patterns of Pritchard-Salamon Realizations. Integral Equations and Operator Theory 27 (1997), 497-501
20. ∞-Control for Infinite-Dimensional Systems: A State-Space Approach, Birkhäuser, Boston, 1993
21. VAN KEULEN, B.: Equivalent Conditions for the Solvability of the Nonstandard LQ-Problem for Pritchard-Salamon Systems, SIAM J. Control and Opt. 33 (1995), 1326-1356
22. PAZY, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, Vol. 44, Springer-Verlag, New York, etc., 1983
23. PRITCHARD, A. J., and SALAMON, D.: The Linear Quadratic Optimal Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators, SIAM J. Control and Opt. 25 (1987), 121-144
24. RAN, A. C. M.: Hankel-Norm Approximation for Infinite Dimensional Systems and Wiener-Hopf Factorization. In: R. F. CURTAIN, Ed., Modelling, Robustness and Sensitivity Reduction in Control Systems, 57-69, Springer-Verlag, Berlin, etc., 1987
25. SALAMON, D.: Control and Observation of Neutral Systems. Research Notes in Mathematics, Vol. 91, Pitman, Boston, 1984