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Volumn 50, Issue 1, 2005, Pages 2-18

Nonlinear input-normal realizations based on the differential eigenstructure of hankel operators

Author keywords

Balanced realization; Model reduction; Nonlinear control

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; VARIATIONAL TECHNIQUES;

EID: 12944263566     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2004.840476     Document Type: Article
Times cited : (75)

References (26)
  • 1
    • 0003792312 scopus 로고
    • Upper Saddle River, NJ: Prentice-Hall
    • T. Kailath, Linear Systems. Upper Saddle River, NJ: Prentice-Hall, 1980.
    • (1980) Linear Systems
    • Kailath, T.1
  • 2
  • 3
    • 0019533482 scopus 로고
    • "Principal component analysis in linear systems: Controllability, observability and model reduction"
    • Jan
    • B. C. Moore, "Principal component analysis in linear systems: controllability, observability and model reduction," IEEE Trans. Autom. Control, vol. AC-26, no. 1, pp. 17-32, Jan. 1981.
    • (1981) IEEE Trans. Autom. Control , vol.AC-26 , Issue.1 , pp. 17-32
    • Moore, B.C.1
  • 4
    • 0021441691 scopus 로고
    • "All optimal Hankel-norm approximations of linear multi-variable systems and their l∞ -error bounds"
    • K. Glover, "All optimal Hankel-norm approximations of linear multi-variable systems and their l∞ -error bounds," Int. J. Control vol. 39, pp. 1115-1193, 1984.
    • (1984) Int. J. Control , vol.39 , pp. 1115-1193
    • Glover, K.1
  • 5
    • 0027641967 scopus 로고
    • "Balancing for nonlinear systems"
    • J. M. A. Scherpen, "Balancing for nonlinear systems," Syst. Control Lett., vol. 21, pp. 143-153, 1993.
    • (1993) Syst. Control Lett. , vol.21 , pp. 143-153
    • Scherpen, J.M.A.1
  • 6
    • 0035940637 scopus 로고    scopus 로고
    • "State dependent matrices in quadratic forms"
    • W. S. Gray and J. M. A. Scherpen, "State dependent matrices in quadratic forms," Syst. Control Lett., vol. 44, no. 3, pp. 219-232, 2001.
    • (2001) Syst. Control Lett. , vol.44 , Issue.3 , pp. 219-232
    • Gray, W.S.1    Scherpen, J.M.A.2
  • 7
    • 0034546304 scopus 로고    scopus 로고
    • "Reduction of nonlinear models using balancing of empirical gramians and Galerkin projections"
    • J. Hahn and T. F. Edgar, "Reduction of nonlinear models using balancing of empirical gramians and Galerkin projections," in Proc. Amer. Control Conf., 2000, pp. 2864-2868.
    • (2000) Proc. Amer. Control Conf. , pp. 2864-2868
    • Hahn, J.1    Edgar, T.F.2
  • 8
    • 0037108424 scopus 로고    scopus 로고
    • "An improved method for nonlinear model reduction using balancing of empirical Gramians"
    • J. Hahn, "An improved method for nonlinear model reduction using balancing of empirical Gramians," Comput. Chem. Eng., vol. 26, no. 10, pp. 1379-1397, 2002.
    • (2002) Comput. Chem. Eng. , vol.26 , Issue.10 , pp. 1379-1397
    • Hahn, J.1
  • 10
    • 0003496515 scopus 로고    scopus 로고
    • "Modeling and reduction with applications to semiconductor processing"
    • Ph.D. dissertation, Univ. Maryland, College Park, MD
    • A. J. Newman, "Modeling and reduction with applications to semiconductor processing," Ph.D. dissertation, Univ. Maryland, College Park, MD, 1999.
    • (1999)
    • Newman, A.J.1
  • 11
    • 0036566376 scopus 로고    scopus 로고
    • "A subspace approach to balanced truncation for model reduction of nonlinear systems"
    • S. Lall, J. E. Marsden, and G. Glavaski, "A subspace approach to balanced truncation for model reduction of nonlinear systems," Int. J. Robust Nonlinear Control, vol. 12, no. 6, pp. 519-535, 2002.
    • (2002) Int. J. Robust Nonlinear Control , vol.12 , Issue.6 , pp. 519-535
    • Lall, S.1    Marsden, J.E.2    Glavaski, G.3
  • 13
    • 0033283815 scopus 로고    scopus 로고
    • "On singular value functions and Hankel operators for nonlinear systems"
    • J. M. A. Scherpen and W. S. Gray, "On singular value functions and Hankel operators for nonlinear systems," in Proc. Amer. Control Conf., 1999, pp. 2360-2364.
    • (1999) Proc. Amer. Control Conf. , pp. 2360-2364
    • Scherpen, J.M.A.1    Gray, W.S.2
  • 14
    • 0034442064 scopus 로고    scopus 로고
    • "On Hankel structure, Hilbert adjoints, and Hamiltonian adjoint realizations for nonlinear systems"
    • Proc. 2000 Conf. Decision and Control Sydney, Australia, Dec
    • J. M. A. Scherpen, K. Fujimoto, and W. S. Gray, "On Hankel structure, Hilbert adjoints, and Hamiltonian adjoint realizations for nonlinear systems," in Proc. 2000 Conf. Decision and Control, Sydney, Australia, Dec. 2000, pp. 5102-5107.
    • (2000) , pp. 5102-5107
    • Scherpen, J.M.A.1    Fujimoto, K.2    Gray, W.S.3
  • 15
    • 0003018087 scopus 로고
    • "Nonlinear compact mappings and their adjoints"
    • J. Batt, "Nonlinear compact mappings and their adjoints," Math. Ann., vol. 189, pp. 5-25, 1970.
    • (1970) Math. Ann. , vol.189 , pp. 5-25
    • Batt, J.1
  • 16
    • 0036833128 scopus 로고    scopus 로고
    • "Nonlinear Hilbert adjoints: Properties and applications to Hankel singular value analysis"
    • J. M. A. Scherpen and W. S. Gray, "Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis," Nonlinear Anal.: Theory, Meth., Appl., vol. 51, no. 5, pp. 883-901, 2002.
    • (2002) Nonlinear Anal.: Theory, Meth., Appl. , vol.51 , Issue.5 , pp. 883-901
    • Scherpen, J.M.A.1    Gray, W.S.2
  • 17
    • 0000332769 scopus 로고    scopus 로고
    • "Eigenstructure of nonlinear Hankel operators"
    • ser. Lecture Notes on Control and Information Science, A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, Eds. Paris, France: Springer-Verlag
    • K. Fujimoto and J, M. A. Scherpen, "Eigenstructure of nonlinear Hankel operators," in Nonlinear Control in the Year 2000. ser. Lecture Notes on Control and Information Science, A. Isidori, F. Lamnabhi-Lagarrigue, and W. Respondek, Eds. Paris, France: Springer-Verlag, 2000, vol. 258, pp. 385-398.
    • (2000) Nonlinear Control in the Year 2000 , vol.258 , pp. 385-398
    • Fujimoto, K.1    Scherpen, J.M.A.2
  • 18
    • 0036779202 scopus 로고    scopus 로고
    • "Hamiltonian realizations of nonlinear adjoint operators"
    • K. Fujimoto, J. M. A. Scherpen, and W. S. Gray, "Hamiltonian realizations of nonlinear adjoint operators," Automatica, vol. 38, no. 10, pp. 1769-1775, 2002.
    • (2002) Automatica , vol.38 , Issue.10 , pp. 1769-1775
    • Fujimoto, K.1    Scherpen, J.M.A.2    Gray, W.S.3
  • 19
    • 0003797651 scopus 로고
    • ser. Lecture Notes on Control and Information Science. Berlin, Germany: Springer-Verlag
    • P. E. Crouch and A. J. van der Schaft, Variational and Hamiltonian Control Systems, ser. Lecture Notes on Control and Information Science. Berlin, Germany: Springer-Verlag, 1987, vol. 101.
    • (1987) Variational and Hamiltonian Control Systems , vol.101
    • Crouch, P.E.1    Schaft, A.J.2
  • 20
    • 0030104565 scopus 로고    scopus 로고
    • "J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems"
    • Mar
    • J. A. Ball and A. J. van der Schaft, "J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems," IEEE Trans. Autom. Control, vol. 41, no. 3, pp. 379-392, Mar. 1996.
    • (1996) IEEE Trans. Autom. Control , vol.41 , Issue.3 , pp. 379-392
    • Ball, J.A.1    Schaft, A.J.2
  • 22
    • 0003494036 scopus 로고    scopus 로고
    • "Synthesis and analysis of nonlinear control systems based on transformations and factorizations"
    • Ph.D. dissertation, Kyoto Univ., Kyoto, Japan
    • K. Fujimoto, "Synthesis and analysis of nonlinear control systems based on transformations and factorizations," Ph.D. dissertation, Kyoto Univ., Kyoto, Japan, 2000.
    • (2000)
    • Fujimoto, K.1
  • 25
    • 0034317867 scopus 로고    scopus 로고
    • "Minimality and local state decompositions of a nonlinear state space realization using energy functions"
    • Nov
    • J. M. A. Scherpen and W. S. Gray, "Minimality and local state decompositions of a nonlinear state space realization using energy functions," IEEE Trans. Autom. Control, vol. 45, no. 11, pp. 2079-2086, Nov. 2000.
    • (2000) IEEE Trans. Autom. Control , vol.45 , Issue.11 , pp. 2079-2086
    • Scherpen, J.M.A.1    Gray, W.S.2
  • 26
    • 0004190360 scopus 로고
    • Princeton, NJ: Princeton Univ. Press
    • J. W. Milnor, Morse Theory. Princeton, NJ: Princeton Univ. Press, 1963.
    • (1963) Morse Theory
    • Milnor, J.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.