Keywords
- Orthogonal Projection
- Toeplitz Operator
- Interpolation Problem
- Singular System
- Hankel Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
V.M. Adamjam, D.Z. Arov and M.G. Krein Infinite Hankel matrices and generalized problems of Caratheodory-Fejer and F. Riesz, Functional Anal. Appl. 2(1968), 1–18.
V.M. Adamjam, D.Z. Arov and M.G. Krein, Analytic properties of Schmidt pairs for Hankel operator and the generalized Schur-Takagi problem, Math. USSR-Sb. 15(1972), 31–78.
V.M. Adamjam, D.Z. Arov aned M.G. Krein, Infinite block Hankel matrices and related extension problems, Amer. Math. Soc. Transl. 111(1978), 133–156.
V. Anantharam and C. Desoer, On the stabilization of nonlinear systems, IEEE Trans. Automat. Control, AC-29(1984), 569–573.
J. Ball, C. Foias, J.W. Helton and A. Tannenbaum, On a local nonlinear commutant lifting theorem, I.U. Math. Journal, 36(1987), 693–709.
J. Ball, C. Foias, J.W. Helton and A. Tannenbaum, A Poincaré-Dulac approach to a nonlinear Beurling-Lax-Halmos theorem, J. Math. Anal. Appl., Vol. 139, 2(1989), 496–514.
H. Bercovici, C. Foias and A. Tannenbaum, On skew Toeplitz operators, I, Operator Theory; Adv. Appl., 29(1988), 21–44.
H. Bercovici, Operator theory and arithmetic in H ∞, AMS, Providence, RI, (1988).
S. Boyd and L. Chua, Fading memory and the problem of approximating nonlinear operators with Volterra series, IEEE Trans. Circuits and Systems, CAS-32(1985), 1150–1161.
R.G. Douglas P.S. Muhly and C. Pearcy, Lifting commuting operators, Michigan Math. J., 15(1968), 385–395.
H. Dym and I. Gohberg, A new class of contractive interpolants and maximum entropy principles, Operator Theory: Adv. and Appl., 29(1988), 117–150.
A. Feintuch and B.A. Francis, Uniformally optimal control of linear feedback systems, Automatica, 21(1985), 563–574.
A. Feintuch and B.A. Francis, Distance formulas for operator algebras arising in optimal control problems, Topics in Operator Theory and Interpolation; Operator Theory: Adv. and Appl., 29(1988), 151–179.
C. Foias, Contractive intertwining dilations and waves in layers media, Proceedings of International Congress of Mathematicians, Helsinki, Vol. 2(1978), 605–613.
C. Foias and A. Tannenbaum, On the Nehari problem for a certain class of L∞ functions appearing in control theory, J. Funct. Anal., 74(1987), 146–159.
C. Foias and A. Tannenbaum, Some remarks on optimal interpolation, Systems and Control Letters, 11(1988), 259–264.
C. Foias and A. Tannenbaum, On the four block problem I, Operator Theory: Adv. and Appl., 32(1988), 93–112.
C. Foias and A. Tannenbaum, On the four block problem, II: the singular system, Integral Equ. Oper. Theory, 11(1988), 726–767.
C. Foias and A. Tannenbaum, Weighted optimization theory for nonlinear systems, SIAM J. Control and Optimiz., Vol. 27, 4(1989), 842–860.
C. Foias and A. Tannenbaum, Iterative commutant lifting for systems with rational symbol, Operatory Theory: Adv. and Appl., 41(1989), 255–277.
C. Foias and A. Tannenbaum, A causal commutant lifting theorem and H∞-optimization for nonlinear systems (in preparation).
C. Foias, A. Tannenbaum and G. Zames, On the H∞-optimal sensitivity problem for systems with delays, SIAM J. Control and Optimiz., Vol. 25, 3(1987), 686–705.
C. Foias, A. Tannenbaum and G. Zames, Sensitivity minimization for arbitrary SISO distributed plants, Systems Control Lett., 8(1987), 189–195.
C. Foias, A. Tannenbaum and G. Zames, Some explicit formulae for the singular values of certain Hankel operators with factorizable symbol, SIAM J. Math. Anal., 19(1988), 1081–1089.
B.A. Francis, A course in H ∞ Control Theory, Lecture Notes in Control and Informaion Science, Springer, New York, 1987.
C. Gu, Eliminating the genericity conditions in a skew Toeplitz algorithm for the H∞-optimal sensitivity problem (in preparation).
Z. Nehari, On bounded bilinear forms, Ann. of Math. 65(1957), 153–162.
S. Parrott, Unitary dilations for commuting contractions, Pacific J. Math., 34(1979), 481–490.
M. Rosenblum and J. Rovnyak, Hardy classes and operator theory, Oxford Univ. Press, New York, 1985.
D. Sarason, Generalized interpolation in H∞, Trans. Amer. Math. Soc., 127(1967), 179–203.
B. Sz.-Nagy and C. Foias, Dilation des commutants d'opérateurs, C.R. Acad. Sci. Paris, Ser. A 265(1968), 493–495.
B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970.
B. Sz.-Nagy and C. Foias, The "lifting theorem" for intertwining operators and some new applications, I.U. Math. Journal, 20(1971), 901–904.
G. Zames, Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses, IEEE Trans. Automat. Control, AC-26(1981), 301–320.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Foias, C. (1991). Commutant lifting techniques for computing optimal H∞ controllers. In: Mosca, E., Pandolfi, L. (eds) H∞-Control Theory. Lecture Notes in Mathematics, vol 1496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084466
Download citation
DOI: https://doi.org/10.1007/BFb0084466
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54949-9
Online ISBN: 978-3-540-46604-8
eBook Packages: Springer Book Archive
