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Volumn 130, Issue 6, 2008, Pages 0610041-06100416

A survey/review of frequency-weighted balanced model reduction techniques

Author keywords

[No Author keywords available]

Indexed keywords

BALANCED MODEL REDUCTIONS; COMPUTATIONAL ISSUES; FREQUENCY INTERVALS; GRAMIAN; NUMERICAL EXAMPLES;

EID: 56549090008     PISSN: 00220434     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2977468     Document Type: Review
Times cited : (75)

References (60)
  • 1
    • 0345992962 scopus 로고
    • Techniques in Optimized Model Reduction for High Dimensional Systems
    • Al-Saggaf, U. M., and Bettayeb, M., 1993, "Techniques in Optimized Model Reduction for High Dimensional Systems," Control. Dyn. Syst., 55, pp. 51-106.
    • (1993) Control. Dyn. Syst , vol.55 , pp. 51-106
    • Al-Saggaf, U.M.1    Bettayeb, M.2
  • 2
    • 0019533482 scopus 로고
    • Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction
    • Moore, B. C., 1981, "Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction," IEEE Trans. Autom. Control, AC-26, pp. 17-32.
    • (1981) IEEE Trans. Autom. Control , vol.AC-26 , pp. 17-32
    • Moore, B.C.1
  • 3
    • 0021641650 scopus 로고
    • Model Reduction With Balanced Realizations: An Error Bound and a Frequency Weighted Generalization
    • Las Vegas, December, pp
    • Enns, D. F., 1984, "Model Reduction With Balanced Realizations: An Error Bound and a Frequency Weighted Generalization," Proceedings of Conference on Decision and Control, Las Vegas, December, pp. 127-132.
    • (1984) Proceedings of Conference on Decision and Control , pp. 127-132
    • Enns, D.F.1
  • 4
    • 0024716281 scopus 로고
    • Controller Reduction: Concepts and Approaches
    • Anderson, B. D. O., and Liu, Y., 1989, "Controller Reduction: Concepts and Approaches," IEEE Trans. Autom. Control, AC-34, pp. 802-812.
    • (1989) IEEE Trans. Autom. Control , vol.AC-34 , pp. 802-812
    • Anderson, B.D.O.1    Liu, Y.2
  • 5
    • 0026881010 scopus 로고
    • Model Reduction via Frequency Weighted Balanced Realization
    • Lin, C.-A., and Chiu, T.-Y., 1992, "Model Reduction via Frequency Weighted Balanced Realization," Control Theory Adv. Technol., 8, pp. 341-451.
    • (1992) Control Theory Adv. Technol , vol.8 , pp. 341-451
    • Lin, C.-A.1    Chiu, T.-Y.2
  • 7
    • 0037402067 scopus 로고    scopus 로고
    • Accuracy-Enhancing Methods for Balancing-Related Frequency-Weighted Model and Controller Reduction
    • Varga, A., and Anderson, B. D. O., 2003, "Accuracy-Enhancing Methods for Balancing-Related Frequency-Weighted Model and Controller Reduction," Automatica, 39, pp. 919-927.
    • (2003) Automatica , vol.39 , pp. 919-927
    • Varga, A.1    Anderson, B.D.O.2
  • 8
    • 0032594194 scopus 로고    scopus 로고
    • A New Frequency Weighted Balanced Truncation Method and an Error Bound
    • Wang, G., Sreeram, V., and Liu, W. Q., 1999, "A New Frequency Weighted Balanced Truncation Method and an Error Bound," IEEE Trans. Autom. Control, 44, pp. 1734-1737.
    • (1999) IEEE Trans. Autom. Control , vol.44 , pp. 1734-1737
    • Wang, G.1    Sreeram, V.2    Liu, W.Q.3
  • 9
    • 14244263934 scopus 로고    scopus 로고
    • A New Frequency Weighted Balanced Related Technique With Error Bound
    • Bahamas, Dec. 14-17, pp
    • Sreeram, V., 2004, "A New Frequency Weighted Balanced Related Technique With Error Bound," Proceedings of 43rd IEEE Conference on Decision and Control, Bahamas, Dec. 14-17, pp. 3084-3089.
    • (2004) Proceedings of 43rd IEEE Conference on Decision and Control , pp. 3084-3089
    • Sreeram, V.1
  • 10
    • 0022012962 scopus 로고
    • Frequency Weighted Optimal Hankel-Norm Approximation of Stable Transfer Function
    • Latham, G. A., and Anderson, B. D. O., 1986, "Frequency Weighted Optimal Hankel-Norm Approximation of Stable Transfer Function," Syst. Control Lett., 5, pp. 229-236.
    • (1986) Syst. Control Lett , vol.5 , pp. 229-236
    • Latham, G.A.1    Anderson, B.D.O.2
  • 11
    • 0024051238 scopus 로고
    • Model Reduction via Balanced Realization: An Extension and Frequency Weighted Techniques
    • Al-Saggaf, U. M., and Franklin, G. F., 1988, "Model Reduction via Balanced Realization: An Extension and Frequency Weighted Techniques," IEEE Trans. Autom. Control, AC-33, pp. 687-692.
    • (1988) IEEE Trans. Autom. Control , vol.AC-33 , pp. 687-692
    • Al-Saggaf, U.M.1    Franklin, G.F.2
  • 12
    • 0022736940 scopus 로고
    • Optimal Hankel-Norm Approximation of Stable Systems With First-Order Stable Weighting Functions
    • Hung, Y. S., and Glover, K., 1986, "Optimal Hankel-Norm Approximation of Stable Systems With First-Order Stable Weighting Functions," Syst. Control Lett., 7, pp. 165-172.
    • (1986) Syst. Control Lett , vol.7 , pp. 165-172
    • Hung, Y.S.1    Glover, K.2
  • 13
    • 0027641159 scopus 로고
    • Frequency-Weighted Model Reduction With L-Infinity Error Bounds
    • Zhou, K., 1993, "Frequency-Weighted Model Reduction With L-Infinity Error Bounds," Syst. Control Lett., 21, pp. 115-125.
    • (1993) Syst. Control Lett , vol.21 , pp. 115-125
    • Zhou, K.1
  • 14
    • 0029392245 scopus 로고
    • ∞ Norm Optimal Hankel Norm Model Reduction
    • ∞ Norm Optimal Hankel Norm Model Reduction," IEEE Trans. Autom. Control, 40, pp. 1687-1699.
    • (1995) IEEE Trans. Autom. Control , vol.40 , pp. 1687-1699
    • Zhou, K.1
  • 15
    • 0029517466 scopus 로고
    • Frequency Weighted Balanced Reduction Technique: A Generalization and an Error Bound
    • New Orleans, Dec. 13-15, pp
    • Sreeram, V., and Anderson, B. D., 1995, "Frequency Weighted Balanced Reduction Technique: A Generalization and an Error Bound," Proceedings of 34th IEEE Conference on Decision and Control, New Orleans, Dec. 13-15, pp. 3576-3581.
    • (1995) Proceedings of 34th IEEE Conference on Decision and Control , pp. 3576-3581
    • Sreeram, V.1    Anderson, B.D.2
  • 16
    • 0025385228 scopus 로고
    • Model Reduction in Limited Time and Frequency Intervals
    • Gawronski, W., and Juang, J.-N., 1990, "Model Reduction in Limited Time and Frequency Intervals," Int. J. Syst. Sci., 21(2), pp. 349-376.
    • (1990) Int. J. Syst. Sci , vol.21 , Issue.2 , pp. 349-376
    • Gawronski, W.1    Juang, J.-N.2
  • 17
    • 4544354870 scopus 로고    scopus 로고
    • A Survey of Model Reduction by Balanced Truncation and Some New Results
    • Gugercin, S., and Antoulas, A. C., 2004, "A Survey of Model Reduction by Balanced Truncation and Some New Results," Int. J. Control, 77(8), pp. 748-766.
    • (2004) Int. J. Control , vol.77 , Issue.8 , pp. 748-766
    • Gugercin, S.1    Antoulas, A.C.2
  • 18
    • 0029276443 scopus 로고
    • Structurally Balanced Controller Order Reduction With Guaranteed Closed Loop Performance
    • Zhou, K., D'Souza, C., and Cloutier, J. R., 1995, "Structurally Balanced Controller Order Reduction With Guaranteed Closed Loop Performance," Syst. Control Lett., 24, pp. 235-242.
    • (1995) Syst. Control Lett , vol.24 , pp. 235-242
    • Zhou, K.1    D'Souza, C.2    Cloutier, J.R.3
  • 19
    • 0026850973 scopus 로고
    • A Structured Approximation Problem With Applications to Frequency Weighted Model Reduction
    • Glover, K., Limebeer, D. J. N., and Hung, Y. S., 1992, "A Structured Approximation Problem With Applications to Frequency Weighted Model Reduction," IEEE Trans. Autom. Control, AC-37(4), pp. 947-465.
    • (1992) IEEE Trans. Autom. Control , vol.AC-37 , Issue.4 , pp. 947-465
    • Glover, K.1    Limebeer, D.J.N.2    Hung, Y.S.3
  • 20
    • 0021441691 scopus 로고
    • ∞ - Error Bounds
    • ∞ - Error Bounds," Int. J. Control, 39, pp. 1115-1195.
    • (1984) Int. J. Control , vol.39 , pp. 1115-1195
    • Glover, K.1
  • 21
    • 0037109826 scopus 로고    scopus 로고
    • A Simple Frequency Weighted Model Reduction Using Structurally Balanced Truncation: Existence of Solution
    • Oh, D. C., and Kim, J. H., 2002, "A Simple Frequency Weighted Model Reduction Using Structurally Balanced Truncation: Existence of Solution," Int. J. Control, 75(15), pp. 1190-1195.
    • (2002) Int. J. Control , vol.75 , Issue.15 , pp. 1190-1195
    • Oh, D.C.1    Kim, J.H.2
  • 23
    • 17744399597 scopus 로고    scopus 로고
    • On Frequency Weighted Balanced Truncation: Hankel Singular Values and Error Bounds
    • Gestel, T. V., Moore, B. D., Anderson, B. D. O., and Overschee, P. V., 2001, "On Frequency Weighted Balanced Truncation: Hankel Singular Values and Error Bounds," Eur. J. Control, 7, pp. 584-592.
    • (2001) Eur. J. Control , vol.7 , pp. 584-592
    • Gestel, T.V.1    Moore, B.D.2    Anderson, B.D.O.3    Overschee, P.V.4
  • 24
    • 23944507612 scopus 로고    scopus 로고
    • Frequency Weighted Model Reduction Technique With Error Bounds
    • Portland, June 8-10, pp
    • Sreeram, V., and Ghafoor, A., 2005, "Frequency Weighted Model Reduction Technique With Error Bounds," Proceedings of American Control Conference, Portland, June 8-10, pp. 2584-2589.
    • (2005) Proceedings of American Control Conference , pp. 2584-2589
    • Sreeram, V.1    Ghafoor, A.2
  • 25
    • 0036349313 scopus 로고    scopus 로고
    • On the Properties of Frequency Weighted Balanced Truncation Techniques
    • Anchorage, AK, May 8-10, pp
    • Sreeram, V., 2002, "On the Properties of Frequency Weighted Balanced Truncation Techniques," Proceedings of 2002 American Control Conference, Anchorage, AK, May 8-10, pp. 1153-1154.
    • (2002) Proceedings of 2002 American Control Conference , pp. 1153-1154
    • Sreeram, V.1
  • 26
    • 0029255267 scopus 로고
    • Error Bound for Transfer Function Order Reduction Using Frequency Weighted Balanced Truncation
    • Kim, S. W., Anderson, B. D. O., and Medievski, A. G., 1995, "Error Bound for Transfer Function Order Reduction Using Frequency Weighted Balanced Truncation," Syst. Control Lett., 24, pp. 183-192.
    • (1995) Syst. Control Lett , vol.24 , pp. 183-192
    • Kim, S.W.1    Anderson, B.D.O.2    Medievski, A.G.3
  • 27
    • 0029640099 scopus 로고
    • Multiplicative Approximation of Transfer Function With Frequency Weighting
    • Kim, S. W., Anderson, B. D. O., and Medievski, A. G., 1995, "Multiplicative Approximation of Transfer Function With Frequency Weighting," Syst. Control Lett., 25, pp. 199-204.
    • (1995) Syst. Control Lett , vol.25 , pp. 199-204
    • Kim, S.W.1    Anderson, B.D.O.2    Medievski, A.G.3
  • 28
    • 0029469008 scopus 로고
    • ∞ Model Reduction via Linear Matrix Inequalities: Continuous and Discrete Time Cases
    • ∞ Model Reduction via Linear Matrix Inequalities: Continuous and Discrete Time Cases," Syst. Control Lett., 26, pp. 321-333.
    • (1995) Syst. Control Lett , vol.26 , pp. 321-333
    • Grigoriadis, K.M.1
  • 29
    • 12344321639 scopus 로고    scopus 로고
    • Using Controller Reduction Techniques for Efficient PID Controller Synthesis
    • Ukpai, U. I., and Jayasuriya, S., 2004, "Using Controller Reduction Techniques for Efficient PID Controller Synthesis," ASME J. Dyn. Syst., Meas., Control, 26, pp. 692-695.
    • (2004) ASME J. Dyn. Syst., Meas., Control , vol.26 , pp. 692-695
    • Ukpai, U.I.1    Jayasuriya, S.2
  • 30
    • 43049173308 scopus 로고    scopus 로고
    • Dimension Reduction of Large-Scale Systems
    • P. Benner, V. Mehrmann, and D. Sorensen, eds, Springer-Verlag, Berlin
    • 2005, Dimension Reduction of Large-Scale Systems (Lecture Notes in Computational Science and Engineering Vol. 45), P. Benner, V. Mehrmann, and D. Sorensen, eds., Springer-Verlag, Berlin.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.45
  • 32
    • 33847213015 scopus 로고    scopus 로고
    • On Model Reduction of Structured Systems
    • Dimension Reduction of Large-Scale Systems , P. Benner, V. Mehrmann, and D. C. Sorensen, eds, Springer-Verlag, Berlin, pp
    • Sorensen, D. C., and Antoulas, A. C., 2005, "On Model Reduction of Structured Systems," Dimension Reduction of Large-Scale Systems (Lecture Notes in Computational Science and Engineering Vol. 45), P. Benner, V. Mehrmann, and D. C. Sorensen, eds., Springer-Verlag, Berlin, pp. 117-130.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.45 , pp. 117-130
    • Sorensen, D.C.1    Antoulas, A.C.2
  • 33
    • 0007942236 scopus 로고    scopus 로고
    • Model Reduction for Control Design,
    • Ph.D. thesis, KU Leuven, Belgium
    • Schelfhout, G., 1996, "Model Reduction for Control Design," Ph.D. thesis, KU Leuven, Belgium.
    • (1996)
    • Schelfhout, G.1
  • 34
    • 0008296147 scopus 로고    scopus 로고
    • Model Reduction Software in the SLICOT Library
    • Applied and Computational Control, Signals, and Circuits , B. N. Dana, ed, Kluwer Academic, Boston, MA, pp
    • Varga, A., 2001, "Model Reduction Software in the SLICOT Library," Applied and Computational Control, Signals, and Circuits (The Kluwer International Series in Engineering and Computer Science Vol. 629), B. N. Dana, ed., Kluwer Academic, Boston, MA, pp. 239-282.
    • (2001) The Kluwer International Series in Engineering and Computer Science , vol.629 , pp. 239-282
    • Varga, A.1
  • 35
    • 56549106682 scopus 로고    scopus 로고
    • Controller Reduction Using Accuracy-Enhancing Methods
    • Dimension Reduction of Large-Scale Systems , P. Benner, V. Mehrmann, and D. C. Sorensen, eds, Springer-Verlag, Berlin, pp
    • Varga, A., 2005, "Controller Reduction Using Accuracy-Enhancing Methods," Dimension Reduction of Large-Scale Systems (Lecture Notes in Computational Science and Engineering Vol. 45), P. Benner, V. Mehrmann, and D. C. Sorensen, eds., Springer-Verlag, Berlin, pp. 225-260.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.45 , pp. 225-260
    • Varga, A.1
  • 36
    • 0020114118 scopus 로고
    • Model Reduction via Balanced State Space Representations
    • Pernebo, L., and Silverman, L. M., 1982, "Model Reduction via Balanced State Space Representations," IEEE Trans. Autom. Control, AC-27, pp. 382-387.
    • (1982) IEEE Trans. Autom. Control , vol.AC-27 , pp. 382-387
    • Pernebo, L.1    Silverman, L.M.2
  • 37
    • 0023439931 scopus 로고
    • Truncated Balanced Realization of a Stable Non-Minimal State-Space System
    • Tombs, M. S., and Postlethwaite, I., 1987, "Truncated Balanced Realization of a Stable Non-Minimal State-Space System," Int. J. Control, 46, pp. 1319-1330.
    • (1987) Int. J. Control , vol.46 , pp. 1319-1330
    • Tombs, M.S.1    Postlethwaite, I.2
  • 39
    • 0001249457 scopus 로고
    • Singular Perturbation Model Reduction of Balanced Systems
    • Fernando, K. V., and Nicholson, H., 1982, "Singular Perturbation Model Reduction of Balanced Systems," IEEE Trans. Autom. Control, 27, pp. 466-468.
    • (1982) IEEE Trans. Autom. Control , vol.27 , pp. 466-468
    • Fernando, K.V.1    Nicholson, H.2
  • 40
    • 0024750490 scopus 로고
    • Singular Perturbation Approximation of Balanced Systems
    • Liu, Y., and Anderson, B. D. O., 1989, "Singular Perturbation Approximation of Balanced Systems," Int. J. Control, 50, pp. 1379-1404.
    • (1989) Int. J. Control , vol.50 , pp. 1379-1404
    • Liu, Y.1    Anderson, B.D.O.2
  • 41
    • 0022147916 scopus 로고
    • Balanced Forms: Canonicity and Parameterizations
    • Kabamba, P. T., 1985, "Balanced Forms: Canonicity and Parameterizations," IEEE Trans. Autom. Control, AC-30(113), pp. 1106-1109.
    • (1985) IEEE Trans. Autom. Control , vol.AC-30 , Issue.113 , pp. 1106-1109
    • Kabamba, P.T.1
  • 44
    • 0021542280 scopus 로고
    • A Transformation Approach to Stochastic Model Reduction
    • Desai, U. B., and Pal, D., 1984, "A Transformation Approach to Stochastic Model Reduction," IEEE Trans. Autom. Control, AC-29(12), pp. 1097-1100.
    • (1984) IEEE Trans. Autom. Control , vol.AC-29 , Issue.12 , pp. 1097-1100
    • Desai, U.B.1    Pal, D.2
  • 45
    • 0000921740 scopus 로고
    • Balanced Stochastic Realization
    • Green, M., 1988, "Balanced Stochastic Realization," Linear Algebr. Appl., 98, pp. 211-247.
    • (1988) Linear Algebr. Appl , vol.98 , pp. 211-247
    • Green, M.1
  • 47
    • 0027701150 scopus 로고
    • Discrete-Time Model Reduction in Limited Frequency Ranges
    • Horta, L. G., Juang, J. N., and Longman, R. W., 1993, "Discrete-Time Model Reduction in Limited Frequency Ranges," J. Guid. Control Dyn., 16(6), pp. 1125-1130.
    • (1993) J. Guid. Control Dyn , vol.16 , Issue.6 , pp. 1125-1130
    • Horta, L.G.1    Juang, J.N.2    Longman, R.W.3
  • 48
    • 17744387403 scopus 로고    scopus 로고
    • On Frequency Weighted Balanced Truncation Technique Retaining Hankel Singular Values
    • Taipei, Taiwan, Sep. 2-4, pp
    • Ghafoor, A., Sreeram, V., and Treasure, R., 2004, "On Frequency Weighted Balanced Truncation Technique Retaining Hankel Singular Values," IEEE Conference on Control Applications, Taipei, Taiwan, Sep. 2-4, pp. 638-642.
    • (2004) IEEE Conference on Control Applications , pp. 638-642
    • Ghafoor, A.1    Sreeram, V.2    Treasure, R.3
  • 49
    • 56549127141 scopus 로고    scopus 로고
    • http://www.slicot.de/start.php?site=slmodred
  • 50
    • 84964043377 scopus 로고    scopus 로고
    • Varga, A., 2002, Numerical Software in SLICOT for Low Order Controller Design, Proceedings of CCA/CACSD, IEEE Internernational Symposium on Computer-Aided Control System Design, Glasgow, UK, Sep. 18-20, p. S.51-56.
    • Varga, A., 2002, "Numerical Software in SLICOT for Low Order Controller Design," Proceedings of CCA/CACSD, IEEE Internernational Symposium on Computer-Aided Control System Design, Glasgow, UK, Sep. 18-20, p. S.51-56.
  • 51
    • 56549088025 scopus 로고    scopus 로고
    • http://www.mathworks.com/products/robust/
  • 52
    • 0024091263 scopus 로고    scopus 로고
    • Green, M., 1988, A Relative Error Bound for Balanced Stochastic Truncation, IEEE Trans. Autom. Control, AC-3300, pp. 961-965.
    • Green, M., 1988, "A Relative Error Bound for Balanced Stochastic Truncation," IEEE Trans. Autom. Control, AC-3300), pp. 961-965.
  • 53
    • 56549115790 scopus 로고    scopus 로고
    • http://www.ni.com/matrixx/model_reduction.htm
  • 54
    • 0024700032 scopus 로고
    • A Schur Method for Balanced-Truncation Model Reduction
    • Safonov, M. G., and Chiang, R. Y., 1989, "A Schur Method for Balanced-Truncation Model Reduction," IEEE Trans. Autom. Control, 34, pp. 729-733.
    • (1989) IEEE Trans. Autom. Control , vol.34 , pp. 729-733
    • Safonov, M.G.1    Chiang, R.Y.2
  • 55
    • 0000567621 scopus 로고
    • Numerical Solution of the Stable, Non-Negative Definite Lyapunov Equation
    • Hammarling, S. J., 1982, "Numerical Solution of the Stable, Non-Negative Definite Lyapunov Equation," IMA J. Numer. Anal., 2, pp. 303-323.
    • (1982) IMA J. Numer. Anal , vol.2 , pp. 303-323
    • Hammarling, S.J.1
  • 56
    • 56549102834 scopus 로고    scopus 로고
    • Varga, A., 1991, Efficient Minimal Realization Procedure Based on Balancing, Preprints of IMACS Symposium on Modelling and Control of Technological Systems, Lille, France, May 7-10, A. El Moudni, P. Borne, and S. G. Tzafestas, eds., 2. pp. 42-47.
    • Varga, A., 1991, "Efficient Minimal Realization Procedure Based on Balancing," Preprints of IMACS Symposium on Modelling and Control of Technological Systems, Lille, France, May 7-10, A. El Moudni, P. Borne, and S. G. Tzafestas, eds., Vol. 2. pp. 42-47.
  • 57
    • 0004128184 scopus 로고
    • Model Reduction for Control System Design,
    • Ph.D. thesis, Stanford University, CA
    • Enns, D. F., 1984, "Model Reduction for Control System Design," Ph.D. thesis, Stanford University, CA.
    • (1984)
    • Enns, D.F.1
  • 59
    • 0003973412 scopus 로고
    • Frequency-Weighted Balanced Reduction of Closed-Loop Mechanical Servo-Systems,
    • Ph.D. thesis, Delft University of Technology, Delft, The Netherlands
    • Wortelboer, P. M. R., 1994, "Frequency-Weighted Balanced Reduction of Closed-Loop Mechanical Servo-Systems," Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.
    • (1994)
    • Wortelboer, P.M.R.1
  • 60
    • 0026901334 scopus 로고
    • Multiplicativeor Bound for Balanced Stochastic Truncation Model Reduction
    • Wang, W., and Sofonov, M. G., 1992, "Multiplicativeor Bound for Balanced Stochastic Truncation Model Reduction," IEEE Trans. Autom. Control, AC-37(8), pp. 1265-1267.
    • (1992) IEEE Trans. Autom. Control , vol.AC-37 , Issue.8 , pp. 1265-1267
    • Wang, W.1    Sofonov, M.G.2


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