메뉴 건너뛰기




Volumn 52, Issue 2, 2007, Pages 181-196

Model reduction of nonstationary LPV systems

Author keywords

Balanced truncation; Coprime factors reduction; Linear parameter varying (LPV) systems; Model reduction; Time varying systems

Indexed keywords

ERROR ANALYSIS; FACTORIZATION; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING;

EID: 33947360775     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.890480     Document Type: Article
Times cited : (39)

References (29)
  • 1
    • 47249152737 scopus 로고    scopus 로고
    • "Control of nonstationary LPV systems"
    • accepted for publication in
    • M. Farhood and G. E. Dullerud, "Control of nonstationary LPV systems," accepted for publication in Automatica.
    • Automatica
    • Farhood, M.1    Dullerud, G.E.2
  • 2
    • 0029733609 scopus 로고    scopus 로고
    • "Stabilization of uncertain linear systems: An LFT approach"
    • Jan
    • W. M. Lu, K. Zhou, and J. C. Doyle, "Stabilization of uncertain linear systems: An LFT approach," IEEE Trans. Autom. Control, vol. 41, no. 2, pp. 50-65, Jan. 1996.
    • (1996) IEEE Trans. Autom. Control , vol.41 , Issue.2 , pp. 50-65
    • Lu, W.M.1    Zhou, K.2    Doyle, J.C.3
  • 3
    • 0028379059 scopus 로고
    • "Gain scheduling via linear fractional transformations"
    • A. Packard, "Gain scheduling via linear fractional transformations," Syst. Control Lett., vol. 22, pp. 79-92, 1994.
    • (1994) Syst. Control Lett. , vol.22 , pp. 79-92
    • Packard, A.1
  • 4
    • 0038576712 scopus 로고    scopus 로고
    • "Error-bounds for balanced model-reduction of linear time-varying systems"
    • Jun
    • S. Lall and C. Beck, "Error-bounds for balanced model-reduction of linear time-varying systems," IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 946-956, Jun. 2003.
    • (2003) IEEE Trans. Autom. Control , vol.48 , Issue.6 , pp. 946-956
    • Lall, S.1    Beck, C.2
  • 5
    • 1442264260 scopus 로고    scopus 로고
    • "Balanced truncation of linear time-varying systems"
    • Feb
    • H. Sandberg and A. Rantzer, "Balanced truncation of linear time-varying systems," IEEE Trans. Autom. Control, vol. 49, no. 2, pp. 217-229, Feb. 2004.
    • (2004) IEEE Trans. Autom. Control , vol.49 , Issue.2 , pp. 217-229
    • Sandberg, H.1    Rantzer, A.2
  • 6
    • 0031364842 scopus 로고    scopus 로고
    • "Model reduction methods for unstable uncertain systems"
    • C. L. Beck and P. Bendottii, "Model reduction methods for unstable uncertain systems," in Proc. IEEE Conf. Decision Control, 1997, vol. 4, pp. 3298-3303.
    • (1997) Proc. IEEE Conf. Decision Control , vol.4 , pp. 3298-3303
    • Beck, C.L.1    Bendottii, P.2
  • 7
    • 30844431538 scopus 로고    scopus 로고
    • "Coprime factors reduction methods for linear parameter varying and uncertain systems"
    • C. Beck, "Coprime factors reduction methods for linear parameter varying and uncertain systems," Syst. Control Lett., vol. 55, pp. 199-213, 2006.
    • (2006) Syst. Control Lett. , vol.55 , pp. 199-213
    • Beck, C.1
  • 8
    • 0025680298 scopus 로고
    • "Fractional balanced reduction: Model reduction via fractional representation"
    • Dec
    • D. G. Meyer, "Fractional balanced reduction: Model reduction via fractional representation," IEEE Trans. Autom. Control, vol. 35, no. 12, pp. 1341-1345, Dec. 1990.
    • (1990) IEEE Trans. Autom. Control , vol.35 , Issue.12 , pp. 1341-1345
    • Meyer, D.G.1
  • 9
    • 0030258250 scopus 로고    scopus 로고
    • "Model reduction of multidimensional and uncertain systems"
    • Oct
    • C. L. Beck, J. C. Doyle, and K. Glover, "Model reduction of multidimensional and uncertain systems," IEEE Trans. Autom. Control, vol. 41, no. 10, pp. 1466-1477, Oct. 1996.
    • (1996) IEEE Trans. Autom. Control , vol.41 , Issue.10 , pp. 1466-1477
    • Beck, C.L.1    Doyle, J.C.2    Glover, K.3
  • 10
    • 0025405107 scopus 로고
    • "An improved error estimate for reduced-order models of discrete-time systems"
    • Mar
    • D. Hinrichsen and A. J. Pritchard, "An improved error estimate for reduced-order models of discrete-time systems," IEEE Trans. Autom. Control, vol. 35, no. 3, pp. 317-320, Mar. 1990.
    • (1990) IEEE Trans. Autom. Control , vol.35 , Issue.3 , pp. 317-320
    • Hinrichsen, D.1    Pritchard, A.J.2
  • 11
    • 0019533482 scopus 로고
    • "Principal component analysis in linear systems: Controllability, observability, and model reduction"
    • Feb
    • B. Moore, "Principal component analysis in linear systems: Controllability, observability, and model reduction," IEEE Trans. Autom. Control, vol. AC-26, no. 1, pp. 17-32, Feb. 1981.
    • (1981) IEEE Trans. Autom. Control , vol.AC-26 , Issue.1 , pp. 17-32
    • Moore, B.1
  • 12
    • 0021641650 scopus 로고
    • "Model reduction with balanced realizations: An error bound and a frequency weighted generalization"
    • D. Enns, "Model reduction with balanced realizations: An error bound and a frequency weighted generalization," in Proc. IEEE Conf. Decision Control, 1984, pp. 127-132.
    • (1984) Proc. IEEE Conf. Decision Control , pp. 127-132
    • Enns, D.1
  • 13
    • 0021441691 scopus 로고
    • ∞ error bounds"
    • ∞ error bounds," Int. J. Control, vol. 39, pp. 1115-1193, 1984.
    • (1984) Int. J. Control , vol.39 , pp. 1115-1193
    • Glover, K.1
  • 14
    • 0033321099 scopus 로고    scopus 로고
    • "A new approach to analysis and synthesis of time-varying systems"
    • Aug
    • G. E. Dullerud and S. G. Lall, "A new approach to analysis and synthesis of time-varying systems," IEEE Trans. Autom. Control, vol. 44, no. 8, pp. 1486-1497, Aug. 1999.
    • (1999) IEEE Trans. Autom. Control , vol.44 , Issue.8 , pp. 1486-1497
    • Dullerud, G.E.1    Lall, S.G.2
  • 15
    • 0000684072 scopus 로고
    • "A frequency theorem for the case in which the state and control spaces are Hilbert spaces with an application to some problems of synthesis of optimal controls"
    • (English translation in Siberian Mathematics Journal)
    • V. A. Yacubovich, "A frequency theorem for the case in which the state and control spaces are Hilbert spaces with an application to some problems of synthesis of optimal controls," Sibirskii Mat. Zh., vol. 15, pp. 639-668, 1975, (English translation in Siberian Mathematics Journal).
    • (1975) Sibirskii Mat. Zh. , vol.15 , pp. 639-668
    • Yacubovich, V.A.1
  • 16
    • 33244489639 scopus 로고    scopus 로고
    • "On the balanced truncation of LTV systems"
    • Feb
    • M. Farhood and G. E. Dullerud, "On the balanced truncation of LTV systems," IEEE Trans. Autom. Control, vol. 51, no. 2, pp. 315-320, Feb. 2006.
    • (2006) IEEE Trans. Autom. Control , vol.51 , Issue.2 , pp. 315-320
    • Farhood, M.1    Dullerud, G.E.2
  • 17
    • 0037121524 scopus 로고    scopus 로고
    • "LMI tools for eventually periodic systems"
    • Dec
    • M. Farhood and G. E. Dullerud, "LMI tools for eventually periodic systems," Syst. Control Lett., vol. 47, no. 5, pp. 417-432, Dec. 2002.
    • (2002) Syst. Control Lett. , vol.47 , Issue.5 , pp. 417-432
    • Farhood, M.1    Dullerud, G.E.2
  • 18
    • 8744291810 scopus 로고    scopus 로고
    • 2-induced control for eventually periodic systems"
    • 2-induced control for eventually periodic systems," in Proc. Amer. Control Conf., 2004, vol. 3, pp. 2021-2026.
    • (2004) Proc. Amer. Control Conf. , vol.3 , pp. 2021-2026
    • Farhood, M.1    Dullerud, G.E.2
  • 19
    • 24944536855 scopus 로고    scopus 로고
    • "Duality and eventually periodic systems"
    • M. Farhood and G. E. Dullerud, "Duality and eventually periodic systems," Int. J. Robust Non-linear Control, vol. 15, no. 13, pp. 575-599, 2005.
    • (2005) Int. J. Robust Non-linear Control , vol.15 , Issue.13 , pp. 575-599
    • Farhood, M.1    Dullerud, G.E.2
  • 20
    • 0031109201 scopus 로고    scopus 로고
    • "On the discretization of LMI-synthesized linear parameter-varying controllers"
    • P. Apkarian, "On the discretization of LMI-synthesized linear parameter-varying controllers," Automatica, vol. 33, pp. 655-661, 1997.
    • (1997) Automatica , vol.33 , pp. 655-661
    • Apkarian, P.1
  • 21
    • 0033296299 scopus 로고    scopus 로고
    • "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones"
    • [Online]. Available: ver. 1.05
    • J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Meth. Software vol. 11-12, pp. 625-653, 1999 [Online]. Available: http://fewcal.kub.n1/sturm, ver. 1.05
    • (1999) Optim. Meth. Software , vol.11-12 , pp. 625-653
    • Sturm, J.F.1
  • 23
    • 0031272805 scopus 로고    scopus 로고
    • "NP-hardness of some linear control design problems"
    • V. Blondel and J. N. Tsitsiklis, "NP-hardness of some linear control design problems," SIAM J. Control Optim., vol. 35, no. 6, pp. 2118-2127, 1997.
    • (1997) SIAM J. Control Optim. , vol.35 , Issue.6 , pp. 2118-2127
    • Blondel, V.1    Tsitsiklis, J.N.2
  • 24
    • 0031197472 scopus 로고    scopus 로고
    • "A cone complementarity linearization algorithm for static output-feedback and related problems"
    • Aug
    • L. E. Ghaoui, F. Oustry, and M. AitRami, "A cone complementarity linearization algorithm for static output-feedback and related problems," IEEE Trans. Autom. Control, vol. 42, no. 8, pp. 1171-1176, Aug. 1997.
    • (1997) IEEE Trans. Autom. Control , vol.42 , Issue.8 , pp. 1171-1176
    • Ghaoui, L.E.1    Oustry, F.2    AitRami, M.3
  • 25
    • 0035661982 scopus 로고    scopus 로고
    • ∞ output feedback controllers"
    • ∞ output feedback controllers," SIAM J. Control Optim., vol. 39, no. 6, pp. 1711-1735, 2001.
    • (2001) SIAM J. Control Optim. , vol.39 , Issue.6 , pp. 1711-1735
    • Leibfritz, F.1
  • 27
    • 31144457450 scopus 로고    scopus 로고
    • "A case study in model reduction of linear time-varying systems"
    • H. Sandberg, "A case study in model reduction of linear time-varying systems," Automatica, vol. 42, pp. 467-472, 2006.
    • (2006) Automatica , vol.42 , pp. 467-472
    • Sandberg, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.