메뉴 건너뛰기




Volumn 1, Issue 6, 2007, Pages 1726-1735

Linear matrix inequality characterisation for ∞ and 2 guaranteed cost gain-scheduling quadratic stabilisation of linear time-varying polytopic systems

Author keywords

[No Author keywords available]

Indexed keywords

COST FUNCTIONS; FEEDBACK CONTROL; LINEAR SYSTEMS; PARAMETER ESTIMATION; THEOREM PROVING; TIME VARYING CONTROL SYSTEMS;

EID: 36248962611     PISSN: 17518644     EISSN: 17518652     Source Type: Journal    
DOI: 10.1049/iet-cta:20070037     Document Type: Article
Times cited : (25)

References (46)
  • 1
    • 0022111023 scopus 로고
    • Necessary and sufficient conditions for quadratic stabilisability of an uncertain system
    • 0022-3239
    • Barmish, B.R.: ' Necessary and sufficient conditions for quadratic stabilisability of an uncertain system ', J. Optim. Theory Appl., 1985, 46, (4), p. 399-408 0022-3239
    • (1985) J. Optim. Theory Appl. , vol.46 , Issue.4 , pp. 399-408
    • Barmish, B.R.1
  • 2
    • 0024699749 scopus 로고
    • A linear programming oriented procedure for quadratic stabilisation of uncertain systems
    • 10.1016/0167-6911(89)90022-4 0167-6911
    • Bernussou, J., Peres, P.L.D., and Geromel, J.C.: ' A linear programming oriented procedure for quadratic stabilisation of uncertain systems ', Syst. Control Lett., 1989, 13, (1), p. 65-72 10.1016/0167-6911(89)90022-4 0167-6911
    • (1989) Syst. Control Lett. , vol.13 , Issue.1 , pp. 65-72
    • Bernussou, J.1    Peres, P.L.D.2    Geromel, J.C.3
  • 4
    • 0026895407 scopus 로고
    • 2 guaranteed cost control for uncertain continuous-time linear systems
    • 10.1016/0167-6911(92)90035-Q 0167-6911
    • 2 guaranteed cost control for uncertain continuous-time linear systems ', Syst. Control Lett., 1992, 19, (1), p. 23-27 10.1016/0167-6911(92)90035-Q 0167-6911
    • (1992) Syst. Control Lett. , vol.19 , Issue.1 , pp. 23-27
    • Geromel, J.C.1    Peres, P.L.D.2    Souza, S.R.3
  • 5
    • 0026189473 scopus 로고
    • ∞ control: A convex optimisation approach
    • 10.1109/9.85062 0018-9286
    • ∞ control: a convex optimisation approach ', IEEE Trans. Autom. Control, 1991, 36, (7), p. 824-837 10.1109/9.85062 0018-9286
    • (1991) IEEE Trans. Autom. Control , vol.36 , Issue.7 , pp. 824-837
    • Khargonekar, P.P.1    Rotea, M.A.2
  • 6
    • 0027608310 scopus 로고
    • ∞ guaranteed cost control for uncertain continuous-time linear systems
    • 10.1016/0167-6911(93)90102-C 0167-6911
    • ∞ guaranteed cost control for uncertain continuous-time linear systems ', Syst. Control Lett., 1993, 20, (6), p. 413-418 10.1016/0167-6911(93)90102-C 0167-6911
    • (1993) Syst. Control Lett. , vol.20 , Issue.6 , pp. 413-418
    • Peres, P.L.D.1    Geromel, J.C.2    Souza, S.R.3
  • 7
    • 0031191562 scopus 로고    scopus 로고
    • Multiobjective output-feedback control via LMI optimisation
    • 10.1109/9.599969 0018-9286
    • Scherer, C., Gahinet, P., and Chilali, M.: ' Multiobjective output-feedback control via LMI optimisation ', IEEE Trans. Autom. Control, 1997, 42, (7), p. 896-911 10.1109/9.599969 0018-9286
    • (1997) IEEE Trans. Autom. Control , vol.42 , Issue.7 , pp. 896-911
    • Scherer, C.1    Gahinet, P.2    Chilali, M.3
  • 9
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • URL:http://sedumi.mcmaster.ca/
    • Sturm, J.F.: ' Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones ', Optim. Methods Softw., 1999, 11-12, p. 625-653, URL:http://sedumi.mcmaster.ca/
    • (1999) Optim. Methods Softw. , vol.11-12 , pp. 625-653
    • Sturm, J.F.1
  • 10
    • 16244419436 scopus 로고    scopus 로고
    • Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach
    • 10.1109/TAC.2005.843848 0018-9286
    • Chesi, G., Garulli, A., Tesi, A., and Vicino, A.: ' Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: an LMI approach ', IEEE Trans. Autom. Control, 2005, 50, (3), p. 365-370 10.1109/TAC.2005.843848 0018-9286
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.3 , pp. 365-370
    • Chesi, G.1    Garulli, A.2    Tesi, A.3    Vicino, A.4
  • 11
    • 24944500782 scopus 로고    scopus 로고
    • A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence
    • 10.1016/j.sysconle.2005.02.015 0167-6911
    • de Oliveira, M.C., and Geromel, J.C.: ' A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence ', Syst. Control Lett., 2005, 54, p. 1131-1134 10.1016/j.sysconle.2005.02.015 0167-6911
    • (2005) Syst. Control Lett. , vol.54 , pp. 1131-1134
    • De Oliveira, M.C.1    Geromel, J.C.2
  • 14
    • 2042449070 scopus 로고    scopus 로고
    • ∞ guaranteed cost computation by means of parameter dependent Lyapunov functions
    • 10.1016/j.automatica.2004.01.025 0005-1098
    • ∞ guaranteed cost computation by means of parameter dependent Lyapunov functions ', Automatica, 2004, 40, (6), p. 1053-1061 10.1016/j.automatica.2004.01.025 0005-1098
    • (2004) Automatica , vol.40 , Issue.6 , pp. 1053-1061
    • De Oliveira, P.J.1    Oliveira, R.C.L.F.2    Leite, V.J.S.3    Montagner, V.F.4    Peres, P.L.D.5
  • 15
    • 17444418964 scopus 로고    scopus 로고
    • A simple and less conservative test for D-stability
    • 0895-4798
    • Oliveira, R.C.L.F., and Peres, P.L.D.: ' A simple and less conservative test for D-stability ', SIAM J. Matrix Anal. Appl., 2005, 26, (2), p. 415-425 0895-4798
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , Issue.2 , pp. 415-425
    • Oliveira, R.C.L.F.1    Peres, P.L.D.2
  • 16
    • 21244436060 scopus 로고    scopus 로고
    • Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: Asymptotically exact LMI conditions
    • Oliveira, R.C.L.F., and Peres, P.L.D.: ' Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: asymptotically exact LMI conditions ', Linear Algebra Appl., 2005, 405, p. 209-228
    • (2005) Linear Algebra Appl. , vol.405 , pp. 209-228
    • Oliveira, R.C.L.F.1    Peres, P.L.D.2
  • 17
    • 28444472732 scopus 로고    scopus 로고
    • LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions
    • 10.1016/j.sysconle.2005.05.003 0167-6911
    • Oliveira, R.C.L.F., and Peres, P.L.D.: ' LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions ', Syst. Control Lett., 2006, 55, (1), p. 52-61 10.1016/j.sysconle.2005.05.003 0167-6911
    • (2006) Syst. Control Lett. , vol.55 , Issue.1 , pp. 52-61
    • Oliveira, R.C.L.F.1    Peres, P.L.D.2
  • 18
    • 0002588085 scopus 로고    scopus 로고
    • A new robust D-stability condition for real convex polytopic uncertainty
    • 10.1016/S0167-6911(99)00119-X 0167-6911
    • Peaucelle, D., Arzelier, D., Bachelier, O., and Bernussou, J.: ' A new robust D-stability condition for real convex polytopic uncertainty ', Syst. Control Lett., 2000, 40, (1), p. 21-30 10.1016/S0167-6911(99)00119-X 0167-6911
    • (2000) Syst. Control Lett. , vol.40 , Issue.1 , pp. 21-30
    • Peaucelle, D.1    Arzelier, D.2    Bachelier, O.3    Bernussou, J.4
  • 19
    • 33845934993 scopus 로고    scopus 로고
    • Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions
    • 10.1016/j.automatica.2006.08.024 0005-1098
    • Chesi, G., Garulli, A., Tesi, A., and Vicino, A.: ' Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions ', Automatica, 2007, 43, (2), p. 309-316 10.1016/j.automatica.2006.08. 024 0005-1098
    • (2007) Automatica , vol.43 , Issue.2 , pp. 309-316
    • Chesi, G.1    Garulli, A.2    Tesi, A.3    Vicino, A.4
  • 21
    • 0344494814 scopus 로고    scopus 로고
    • 2 analysis and control of linear parameter-dependent systems
    • 10.1049/ip-cta:20030709 1350-2379
    • 2 analysis and control of linear parameter-dependent systems ', IEE Proc., Control Theory Appl., 2003, 150, (5), p. 501-508 10.1049/ip-cta:20030709 1350-2379
    • (2003) IEE Proc., Control Theory Appl. , vol.150 , Issue.5 , pp. 501-508
    • De Souza, C.E.1    Trofino, A.2    De Oliveira, J.3
  • 22
    • 28444479787 scopus 로고    scopus 로고
    • Robust stability of time varying polytopic systems
    • 10.1016/j.sysconle.2004.11.016 0167-6911
    • Geromel, J.C., and Colaneri, P.: ' Robust stability of time varying polytopic systems ', Syst. Control Lett., 2006, 55, (1), p. 81-85 10.1016/j.sysconle.2004.11.016 0167-6911
    • (2006) Syst. Control Lett. , vol.55 , Issue.1 , pp. 81-85
    • Geromel, J.C.1    Colaneri, P.2
  • 23
    • 9644268034 scopus 로고    scopus 로고
    • ∞ performance of linear time-varying systems in polytopic domains
    • 10.1080/00207170412331319321 0020-7179
    • ∞ performance of linear time-varying systems in polytopic domains ', Int. J. Control, 2004, 77, (15), p. 1343-1352 10.1080/ 00207170412331319321 0020-7179
    • (2004) Int. J. Control , vol.77 , Issue.15 , pp. 1343-1352
    • Montagner, V.F.1    Peres, P.L.D.2
  • 24
    • 33746169128 scopus 로고    scopus 로고
    • State feedback gain scheduling for linear systems with time-varying parameters
    • Montagner, V.F., and Peres, P.L.D.: ' State feedback gain scheduling for linear systems with time-varying parameters ', J. Dyn. Syst. Meas. Control, Trans. ASME, 2006, 128, (2), p. 365-370
    • (2006) J. Dyn. Syst. Meas. Control, Trans. ASME , vol.128 , Issue.2 , pp. 365-370
    • Montagner, V.F.1    Peres, P.L.D.2
  • 25
    • 0035418163 scopus 로고    scopus 로고
    • Biquadratic stability of uncertain linear systems
    • 10.1109/9.940939 0018-9286
    • Trofino, A., and de Souza, C.E.: ' Biquadratic stability of uncertain linear systems ', IEEE Trans. Autom. Control, 2001, 46, (8), p. 1303-1307 10.1109/9.940939 0018-9286
    • (2001) IEEE Trans. Autom. Control , vol.46 , Issue.8 , pp. 1303-1307
    • Trofino, A.1    De Souza, C.E.2
  • 26
    • 0001761076 scopus 로고    scopus 로고
    • Research on gain scheduling
    • 10.1016/S0005-1098(00)00058-3 0005-1098
    • Rugh, W.J., and Shamma, J.S.: ' Research on gain scheduling ', Automatica, 2000, 36, (10), p. 1401-1425 10.1016/S0005-1098(00)00058-3 0005-1098
    • (2000) Automatica , vol.36 , Issue.10 , pp. 1401-1425
    • Rugh, W.J.1    Shamma, J.S.2
  • 27
    • 0026883988 scopus 로고
    • Gain scheduling: Potential hazards and possible remedies
    • 10.1109/37.165527 0272-1708
    • Shamma, J.S., and Athans, M.: ' Gain scheduling: potential hazards and possible remedies ', IEEE Control Syst. Mag., 1992, 12, (3), p. 101-107 10.1109/37.165527 0272-1708
    • (1992) IEEE Control Syst. Mag. , vol.12 , Issue.3 , pp. 101-107
    • Shamma, J.S.1    Athans, M.2
  • 31
    • 33749555793 scopus 로고    scopus 로고
    • 2 gain scheduled state feedback for LPV system with new LMI formulation
    • 10.1049/ip-cta:20050052 1350-2379
    • 2 gain scheduled state feedback for LPV system with new LMI formulation ', IEE Proc., Control Theory Appl., 2005, 152, (6), p. 693-697 10.1049/ip-cta:20050052 1350-2379
    • (2005) IEE Proc., Control Theory Appl. , vol.152 , Issue.6 , pp. 693-697
    • Xie, W.1
  • 32
    • 11144323103 scopus 로고    scopus 로고
    • Springer-Verlag, Heidelberg, Germany Lecture Notes in Control and Information Science
    • Johansson, M.: ' Piecewise linear control systems - a computational approach ', (Springer-Verlag, Heidelberg, Germany, 2003), 284, Lecture Notes in Control and Information Science
    • (2003) Piecewise Linear Control Systems - A Computational Approach , vol.284
    • Johansson, M.1
  • 33
    • 0035302796 scopus 로고    scopus 로고
    • Parameterized linear matrix inequality techniques in fuzzy control system design
    • 10.1109/91.919253 1063-6706
    • Tuan, H.D., Apkarian, P., Narikiyo, T., and Yamamoto, Y.: ' Parameterized linear matrix inequality techniques in fuzzy control system design ', IEEE Trans. Fuzzy Syst., 2001, 9, (2), p. 324-332 10.1109/91.919253 1063-6706
    • (2001) IEEE Trans. Fuzzy Syst. , vol.9 , Issue.2 , pp. 324-332
    • Tuan, H.D.1    Apkarian, P.2    Narikiyo, T.3    Yamamoto, Y.4
  • 34
    • 1042300599 scopus 로고    scopus 로고
    • An existence result for polynomial solutions of parameter-dependent LMIs
    • 10.1016/j.sysconle.2003.08.001 0167-6911
    • Bliman, P.-A.: ' An existence result for polynomial solutions of parameter-dependent LMIs ', Syst. Control Lett., 2004, 51, (3-4), p. 165-169 10.1016/j.sysconle.2003.08.001 0167-6911
    • (2004) Syst. Control Lett. , vol.51 , Issue.3-4 , pp. 165-169
    • Bliman, P.-A.1
  • 35
    • 36248996921 scopus 로고    scopus 로고
    • Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex
    • San Diego, CA, December
    • Bliman, P.-A., Oliveira, R.C.L.F., Montagner, V.F., and Peres, P.L.D.: ' Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex ', Proc. 45th IEEE Conf. Decision and Control, San Diego, CA, December, 2006, p. 1486-1491
    • (2006) Proc. 45th IEEE Conf. Decision and Control , pp. 1486-1491
    • Bliman, P.-A.1    Oliveira, R.C.L.F.2    Montagner, V.F.3    Peres, P.L.D.4
  • 36
    • 1542380047 scopus 로고    scopus 로고
    • Higher-order relaxations for robust LMI problems with verifications for exactness
    • Maui, HI, USA, December
    • Scherer, C.W.: ' Higher-order relaxations for robust LMI problems with verifications for exactness ', Proc. 42nd IEEE Conf. Decision and Control, Maui, HI, USA, December, 2003, p. 4652-4657
    • (2003) Proc. 42nd IEEE Conf. Decision and Control , pp. 4652-4657
    • Scherer, C.W.1
  • 37
    • 33646254843 scopus 로고    scopus 로고
    • Relaxations for robust linear matrix inequality problems with verifications for exactness
    • 0895-4798
    • Scherer, C.W.: ' Relaxations for robust linear matrix inequality problems with verifications for exactness ', SIAM J. Matrix Anal. Appl., 2005, 27, (2), p. 365-395 0895-4798
    • (2005) SIAM J. Matrix Anal. Appl. , vol.27 , Issue.2 , pp. 365-395
    • Scherer, C.W.1
  • 38
    • 36248949515 scopus 로고    scopus 로고
    • Technical report 2003 http://www.complib.de/
    • ' Description of the benchmark examples in Compleib 1.0 ', Technical report, 2003, http://www.complib.de/
  • 40
    • 0001615805 scopus 로고    scopus 로고
    • Stability tests for constrained linear systems.
    • Reza Moheimani S.O. Springer-Verlag, New York Perspectives in robust control
    • de Oliveira, M.C., and Skelton, R.E.: ' Stability tests for constrained linear systems. ', Reza Moheimani, S.O., Lecture Notes in Control and Information Science, (Springer-Verlag, New York, 2001), 268, Perspectives in robust control, p. 241-257
    • (2001) Lecture Notes in Control and Information Science , vol.268 , pp. 241-257
    • De Oliveira, M.C.1    Skelton, R.E.2
  • 41
    • 34547131293 scopus 로고    scopus 로고
    • Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations
    • 0018-9286
    • Oliveira, R.C.L.F., and Peres, P.L.D.: ' Parameter-dependent LMIs in robust analysis: characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations ', IEEE Trans. Autom. Control, 2007, 52, (7), p. 1334-1340 0018-9286
    • (2007) IEEE Trans. Autom. Control , vol.52 , Issue.7 , pp. 1334-1340
    • Oliveira, R.C.L.F.1    Peres, P.L.D.2
  • 42
    • 0031673619 scopus 로고    scopus 로고
    • Advanced gain-scheduling techniques for uncertain systems
    • 10.1109/87.654874 1063-6536
    • Apkarian, P., and Adams, R.J.: ' Advanced gain-scheduling techniques for uncertain systems ', IEEE Trans. Control Syst. Technol., 1998, 6, (1), p. 21-32 10.1109/87.654874 1063-6536
    • (1998) IEEE Trans. Control Syst. Technol. , vol.6 , Issue.1 , pp. 21-32
    • Apkarian, P.1    Adams, R.J.2
  • 43
    • 0027625673 scopus 로고
    • ∞ controllers to a VSTOL aircraft
    • 10.1109/9.231458 0018-9286
    • ∞ controllers to a VSTOL aircraft ', IEEE Trans. Autom. Control, 1993, 38, (7), p. 1021-1039 10.1109/9.231458 0018-9286
    • (1993) IEEE Trans. Autom. Control , vol.38 , Issue.7 , pp. 1021-1039
    • Hyde, R.A.1    Glover, K.2
  • 44
    • 0037353008 scopus 로고    scopus 로고
    • An improved LMI condition for robust D-stability of uncertain polytopic systems
    • 10.1109/TAC.2003.809167 0018-9286
    • Leite, V.J.S., and Peres, P.L.D.: ' An improved LMI condition for robust D-stability of uncertain polytopic systems ', IEEE Trans. Autom. Control, 2003, 48, (3), p. 500-504 10.1109/TAC.2003.809167 0018-9286
    • (2003) IEEE Trans. Autom. Control , vol.48 , Issue.3 , pp. 500-504
    • Leite, V.J.S.1    Peres, P.L.D.2
  • 45
    • 14244260103 scopus 로고    scopus 로고
    • 2 control of linear parameter varying systems using a parametric Lyapunov function
    • December Bahamas, Paradise Island
    • 2 control of linear parameter varying systems using a parametric Lyapunov function ', Proc. 43rd IEEE Conf. Decision and Control, December, 2004, Bahamas, Paradise Island, p. 2936-2941
    • (2004) Proc. 43rd IEEE Conf. Decision and Control , pp. 2936-2941
    • De Souza, C.E.1    Trofino, A.2
  • 46
    • 33644639492 scopus 로고    scopus 로고
    • 2 controller synthesis for linear parameter varying systems via parameter-dependent Lyapunov functions
    • 10.1002/rnc.1040 1049-8923
    • 2 controller synthesis for linear parameter varying systems via parameter-dependent Lyapunov functions ', Int. J. Robust Nonlinear Control, 2006, 16, (5), p. 243-257 10.1002/rnc.1040 1049-8923
    • (2006) Int. J. Robust Nonlinear Control , vol.16 , Issue.5 , pp. 243-257
    • De Souza, C.E.1    Trofino, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.