메뉴 건너뛰기




Volumn 8, Issue 4, 2010, Pages 1348-1367

Balanced truncation of linear second-order systems: A hamiltonian approach

Author keywords

Balanced truncation; Generalized hamiltonian systems; Hankel norm approximation; Invariant manifolds; Strong confinement; Structure preserving model reduction

Indexed keywords

BALANCED TRUNCATION; GENERALIZED HAMILTONIAN SYSTEMS; HANKEL NORM APPROXIMATIONS; INVARIANT MANIFOLDS; STRONG CONFINEMENT; STRUCTURE-PRESERVING;

EID: 77956763488     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/080732717     Document Type: Article
Times cited : (40)

References (33)
  • 3
    • 33646471966 scopus 로고    scopus 로고
    • Special issue on "order reduction of large-scale systems"
    • P. Benner, R.W. Freund, D.C. Sorensen, and A. Varga, Special issue on "order reduction of large-scale systems", Linear Algebra Appl., 415 (2006), pp. 231-234.
    • (2006) Linear Algebra Appl. , vol.415 , pp. 231-234
    • Benner, P.1    Freund, R.W.2    Sorensen, D.C.3    Varga, A.4
  • 4
    • 0030285070 scopus 로고    scopus 로고
    • Balanced and model reduction for second-order form linear systems
    • D.G. Meyer and S. Srinivasan, Balanced and model reduction for second-order form linear systems, IEEE Trans. Automat. Control, 41 (1996), pp. 1632-1644.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 1632-1644
    • Meyer, D.G.1    Srinivasan, S.2
  • 5
    • 33847184088 scopus 로고    scopus 로고
    • Model reduction of second-order systems
    • Dimension Reduction of Large-Scale Systems, P. Benner, D.C. Sorensen, and V. Mehrmann, eds., Springer, Berlin
    • Y. Chahlaoui, K.A. Gallivan, A. Vandendorpe, and P. Van Dooren, Model reduction of second-order systems, in Dimension Reduction of Large-Scale Systems, Lect. Notes Comput. Sci. Eng. 45, P. Benner, D.C. Sorensen, and V. Mehrmann, eds., Springer, Berlin, 2005, pp. 149-172.
    • (2005) Lect. Notes Comput. Sci. Eng. , vol.45 , pp. 149-172
    • Chahlaoui, Y.1    Gallivan, K.A.2    Vandendorpe, A.3    Van Dooren, P.4
  • 7
    • 53349089857 scopus 로고    scopus 로고
    • Balanced truncation model reduction of second-order systems
    • T. Reis and T. Stykel, Balanced truncation model reduction of second-order systems, Math. Comput. Model. Dyn. Syst., 14 (2008), pp. 391-406.
    • (2008) Math. Comput. Model. Dyn. Syst. , vol.14 , pp. 391-406
    • Reis, T.1    Stykel, T.2
  • 8
    • 51649125386 scopus 로고    scopus 로고
    • Second-order balanced truncation for passive-order reduction of RLCK circuits
    • B. Yan, S.X.-D. Tan, and B. McGaughy, Second-order balanced truncation for passive-order reduction of RLCK circuits, IEEE Trans. Circuits Syst. II, 55 (2008), pp. 942-946.
    • (2008) IEEE Trans. Circuits Syst. II , vol.55 , pp. 942-946
    • Yan, B.1    Tan, S.X.-D.2    McGaughy, B.3
  • 12
    • 0024750490 scopus 로고
    • Singular perturbation approximation of balanced systems
    • Y. Liu and B.D.O. Anderson, Singular perturbation approximation of balanced systems, Internat.J. Control, 50 (1989), pp. 1379-1405. (Pubitemid 20623804)
    • (1989) International Journal of Control , vol.50 , Issue.4 , pp. 1379-1405
    • Liu Yi1    Anderson Brian, D.O.2
  • 14
    • 0034545251 scopus 로고    scopus 로고
    • Singular perturbation analysis of system order reduction via system balancing
    • Z. Gajic and M. Lelic, Singular perturbation analysis of system order reduction via system balancing, in Proceedings of the Fourth American Control Conference, 2000, pp. 2420-2424.
    • (2000) Proceedings of the Fourth American Control Conference , pp. 2420-2424
    • Gajic, Z.1    Lelic, M.2
  • 18
    • 0032120939 scopus 로고    scopus 로고
    • Preservation of passivity during RLC network reduction via split congruence transformations
    • K.J. Kerns and A.T. Yang, Preservation of passivity during RLC network reduction via split congruence transformations, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst., 17 (1998), pp. 582-591.
    • (1998) IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. , vol.17 , pp. 582-591
    • Kerns, K.J.1    Yang, A.T.2
  • 21
    • 0019533482 scopus 로고
    • Principal component analysis in linear systems: Controllability, observability, and model reduction
    • B.C. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Trans. Automat. Control, 26 (1981), pp. 17-32.
    • (1981) IEEE Trans. Automat. Control , vol.26 , pp. 17-32
    • Moore, B.C.1
  • 22
    • 0021441691 scopus 로고
    • All optimal Hankel-norm approximations of linear multivariable systems and their L8-error bounds
    • K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their L8-error bounds, Internat.J. Control, 39 (1984), pp. 1115-1193.
    • (1984) Internat.J. Control , vol.39 , pp. 1115-1193
    • Glover, K.1
  • 23
    • 0021195555 scopus 로고
    • Computing the Kalman decomposition: An optimal method
    • D. Boley, Computing the Kalman decomposition: An optimal method, IEEE Trans. Automat. Control, 29 (1984), pp. 51-53.
    • (1984) IEEE Trans. Automat. Control , vol.29 , pp. 51-53
    • Boley, D.1
  • 24
    • 0023288081 scopus 로고
    • Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
    • A.J. Laub, M.T. Heath, C.C. Paige, and R.C. Ward, Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms, IEEE Trans. Automat. Control, 32 (1987), pp. 115-122.
    • (1987) IEEE Trans. Automat. Control , vol.32 , pp. 115-122
    • Laub, A.J.1    Heath, M.T.2    Paige, C.C.3    Ward, R.C.4
  • 25
    • 0023439931 scopus 로고
    • Truncated balanced realization of a stable non-minimal state-space system
    • M.S. Tombs and I. Postlethwaite, Truncated balanced realization of a stable non-minimal state-space system, Internat.J. Control, 46 (1987), pp. 1319-1330.
    • (1987) Internat.J. Control , vol.46 , pp. 1319-1330
    • Tombs, M.S.1    Postlethwaite, I.2
  • 26
    • 0141865706 scopus 로고    scopus 로고
    • Structure-preserving model reduction for mechanical systems
    • S. Lall, P. Krysl, and S. Glavaski, Structure-preserving model reduction for mechanical systems, Phys. D, 184 (2003), pp. 304-318.
    • (2003) Phys. D , vol.184 , pp. 304-318
    • Lall, S.1    Krysl, P.2    Glavaski, S.3
  • 27
    • 0000559545 scopus 로고
    • Systems of differential equations containing small parameters in the derivatives
    • A.N. Tikhonov, Systems of differential equations containing small parameters in the derivatives, Mat. Sb. (N.S.), 31 (1952), pp. 575-586.
    • (1952) Mat. Sb. (N.S.) , vol.31 , pp. 575-586
    • Tikhonov, A.N.1
  • 28
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • N. Fenichel, Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations, 31 (1979), pp. 53-98.
    • (1979) J. Differential Equations , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 32
    • 84990716831 scopus 로고
    • Stability theory for dissipatively perturbed Hamiltonian systems
    • J.H. Maddocks and M.L. Overton, Stability theory for dissipatively perturbed Hamiltonian systems, Comm. Pure Appl. Math., 48 (1995), pp. 583-610.
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 583-610
    • Maddocks, J.H.1    Overton, M.L.2
  • 33
    • 33646471733 scopus 로고    scopus 로고
    • Benchmark examples for model reduction of linear time invariant dynamical systems
    • P. Benner, D.C. Sorensen, and V. Mehrmann, eds., Springer, Berlin
    • Y. Chahlaoui and P. Van Dooren, Benchmark examples for model reduction of linear time invariant dynamical systems, in Dimension Reduction of Large-Scale Systems, Lect. Notes Comput. Sci. Eng. 45, P. Benner, D.C. Sorensen, and V. Mehrmann, eds., Springer, Berlin, 2005, pp. 379-392.
    • (2005) Dimension Reduction of Large-Scale Systems, Lect. Notes Comput. Sci. Eng. , vol.45 , pp. 379-392
    • Chahlaoui, Y.1    Van Dooren, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.