메뉴 건너뛰기




Volumn 54, Issue 10, 2009, Pages 2410-2416

Parameter-dependent Lyapunov functions for linear systems with constant uncertainties

Author keywords

Parameter dependent Lyapunov function (PDLF)

Indexed keywords

LINEAR TIME INVARIANT SYSTEMS; PARAMETER DEPENDENT LYAPUNOV FUNCTION; PARAMETER-DEPENDENT LYAPUNOV FUNCTION (PDLF); PARAMETER-DEPENDENT LYAPUNOV FUNCTIONS; QUADRATIC DEPENDENCE; QUADRATIC LYAPUNOV FUNCTION; ROBUST STABILITY; SCALINGS; SMALL-GAIN CONDITION; STRUCTURED UNCERTAINTIES; TECHNICAL NOTES; TIME-VARYING PERTURBATIONS;

EID: 70350347457     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2029294     Document Type: Article
Times cited : (8)

References (50)
  • 2
    • 0027205718 scopus 로고
    • The complex structured singular value
    • A. Packard and J. Doyle, "The complex structured singular value," Automatica, vol. 29, no. 1, pp. 71-109, 1993.
    • (1993) Automatica , vol.29 , Issue.1 , pp. 71-109
    • Packard, A.1    Doyle, J.2
  • 3
    • 0020203138 scopus 로고    scopus 로고
    • J. Doyle, Analysis of feedback systems with structured uncertainties, Proc. Inst. Elect. Eng., 129, no. 6, pt. D, pp. 242-250, 1982.
    • J. Doyle, "Analysis of feedback systems with structured uncertainties," Proc. Inst. Elect. Eng., vol. 129, no. 6, pt. D, pp. 242-250, 1982.
  • 4
    • 0020207749 scopus 로고    scopus 로고
    • M. Safonov, Stability margins of diagonally perturbed multivariable feedback systems, Proc. Inst. Elect. Eng., 129, no. 6, pt. D, pp. 251-256, 1982.
    • M. Safonov, "Stability margins of diagonally perturbed multivariable feedback systems," Proc. Inst. Elect. Eng., vol. 129, no. 6, pt. D, pp. 251-256, 1982.
  • 5
    • 0028438885 scopus 로고
    • Computational complexity of μ calculation
    • May
    • R. Braatz, P. Young, J. Doyle, and M. Morari, "Computational complexity of μ calculation," IEEE Trans. Autom. Control, vol. 39, no. 5, pp. 1000-1002, May 1994.
    • (1994) IEEE Trans. Autom. Control , vol.39 , Issue.5 , pp. 1000-1002
    • Braatz, R.1    Young, P.2    Doyle, J.3    Morari, M.4
  • 6
    • 0001790982 scopus 로고
    • The componentwise distance to the nearest singular matrix
    • J. Demmel, "The componentwise distance to the nearest singular matrix," SIAM J. Matrix Anal. Appl., vol. 13, no. 1, pp. 10-19, 1992.
    • (1992) SIAM J. Matrix Anal. Appl , vol.13 , Issue.1 , pp. 10-19
    • Demmel, J.1
  • 8
    • 84938017582 scopus 로고
    • On the input-output stability of time-varying nonlinear feedback systems. Part I: Conditions using concepts of loop gain, conicity, and positivity
    • Apr
    • G. Zames, "On the input-output stability of time-varying nonlinear feedback systems. Part I: Conditions using concepts of loop gain, conicity, and positivity," IEEE Trans. Autom. Control, vol. AC-11, no. 2, pp. 228-238, Apr. 1966.
    • (1966) IEEE Trans. Autom. Control , vol.AC-11 , Issue.2 , pp. 228-238
    • Zames, G.1
  • 9
    • 0028412889 scopus 로고
    • Robust stability with time varying structured uncertainty
    • Apr
    • J. Shamma, "Robust stability with time varying structured uncertainty," IEEE Trans. Autom. Control, vol. 39, no. 4, pp. 714-724, Apr. 1994.
    • (1994) IEEE Trans. Autom. Control , vol.39 , Issue.4 , pp. 714-724
    • Shamma, J.1
  • 10
    • 0022111023 scopus 로고
    • Necessary and sufficient conditions for quadratic stabilizability of an uncertain system
    • B. R. Barmish, "Necessary and sufficient conditions for quadratic stabilizability of an uncertain system," J. Optim. Theory Appl., vol. 46, no. 4, pp. 399-408, 1985.
    • (1985) J. Optim. Theory Appl , vol.46 , Issue.4 , pp. 399-408
    • Barmish, B.R.1
  • 11
    • 0024684650 scopus 로고
    • Structured and simultaneous Lyapunov functions for system stability problems
    • S. Boyd and Q. Yang, "Structured and simultaneous Lyapunov functions for system stability problems," Int. J. Control, vol. 49, no. 6, pp. 243-262, 1989.
    • (1989) Int. J. Control , vol.49 , Issue.6 , pp. 243-262
    • Boyd, S.1    Yang, Q.2
  • 12
    • 0025386095 scopus 로고
    • Quadratic stability with real and complex perturbations
    • Feb
    • A. Packard and J. Doyle, "Quadratic stability with real and complex perturbations," IEEE Trans. Autom. Control, vol. 35, no. 2, pp. 198-201, Feb. 1990.
    • (1990) IEEE Trans. Autom. Control , vol.35 , Issue.2 , pp. 198-201
    • Packard, A.1    Doyle, J.2
  • 16
    • 0029373471 scopus 로고
    • Robust performance against time varying structured perturbations
    • Sep
    • K. Poolla and A. Tikku, "Robust performance against time varying structured perturbations," IEEE Trans. Autom. Control, vol. 40, no. 9, pp. 1589-1602, Sep. 1995.
    • (1995) IEEE Trans. Autom. Control , vol.40 , Issue.9 , pp. 1589-1602
    • Poolla, K.1    Tikku, A.2
  • 17
    • 0029270797 scopus 로고
    • Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis
    • Mar
    • W. Haddad and D. Bernstein, "Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis," IEEE Trans. Autom. Control, vol. 40, no. 3, pp. 536-543, Mar. 1995.
    • (1995) IEEE Trans. Autom. Control , vol.40 , Issue.3 , pp. 536-543
    • Haddad, W.1    Bernstein, D.2
  • 18
    • 0028377254 scopus 로고    scopus 로고
    • S. Dasgupta, G. Chockalingam, B. Anderson, and M. Fu, Lyapunov functions for uncertain systems with applications to the stability of time varying systems, IEEE Trans. Circuits Syst., 41, no. 2, pt. I, pp. 93-106, Feb. 1994.
    • S. Dasgupta, G. Chockalingam, B. Anderson, and M. Fu, "Lyapunov functions for uncertain systems with applications to the stability of time varying systems," IEEE Trans. Circuits Syst., vol. 41, no. 2, pt. I, pp. 93-106, Feb. 1994.
  • 19
    • 0028448271 scopus 로고
    • Parameter-dependent Lyapunov functions and the discrete-time Popov criterion for robust analysis
    • W. Haddad and D. Bernstein, "Parameter-dependent Lyapunov functions and the discrete-time Popov criterion for robust analysis," Automatica vol. 30, no. 6, pp. 1015-1021, 1994.
    • (1994) Automatica , vol.30 , Issue.6 , pp. 1015-1021
    • Haddad, W.1    Bernstein, D.2
  • 20
    • 0029178918 scopus 로고
    • S-procedure for the analysis of control systems with parametric uncertainties via parameter-dependent Lyapunov functions
    • E. Feron, P. Apkarian, and P. Gahinet, "S-procedure for the analysis of control systems with parametric uncertainties via parameter-dependent Lyapunov functions," in Proc. ACC, 1995, pp. 968-972.
    • (1995) Proc. ACC , pp. 968-972
    • Feron, E.1    Apkarian, P.2    Gahinet, P.3
  • 21
    • 0030195747 scopus 로고    scopus 로고
    • Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions
    • Jul
    • E. Feron, P. Apkarian, and P. Gahinet, "Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions," IEEE Trans. Autom. Control, vol. 41, no. 7, pp. 1041-1046, Jul. 1996.
    • (1996) IEEE Trans. Autom. Control , vol.41 , Issue.7 , pp. 1041-1046
    • Feron, E.1    Apkarian, P.2    Gahinet, P.3
  • 22
    • 0030106702 scopus 로고    scopus 로고
    • Affine parameter-dependent Lyapunov functions and real parametric uncertainty
    • Mar
    • P. Gahinet, P. Apkarian, and M. Chilali, "Affine parameter-dependent Lyapunov functions and real parametric uncertainty," IEEE Trans. Autom. Control, vol. 41, no. 3, pp. 436-442, Mar. 1996.
    • (1996) IEEE Trans. Autom. Control , vol.41 , Issue.3 , pp. 436-442
    • Gahinet, P.1    Apkarian, P.2    Chilali, M.3
  • 23
    • 0346703284 scopus 로고    scopus 로고
    • A new discrete-time robust stability condition
    • M. de Oliveira, J. Bernussou, and J. Geromel, "A new discrete-time robust stability condition," Syst. Control Lett., vol. 37, no. 4, pp. 261-265, 1999.
    • (1999) Syst. Control Lett , vol.37 , Issue.4 , pp. 261-265
    • de Oliveira, M.1    Bernussou, J.2    Geromel, J.3
  • 24
    • 0034915492 scopus 로고    scopus 로고
    • Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties
    • J. Daafouz and J. Bernussou, "Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties," Syst. Control Lett., vol. 43, no. 5, pp. 355-359, 2001.
    • (2001) Syst. Control Lett , vol.43 , Issue.5 , pp. 355-359
    • Daafouz, J.1    Bernussou, J.2
  • 25
    • 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
    • M. de Oliveira and J. Geromel, "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., vol. 54, no. 11, pp. 1131-1134, 2005.
    • (2005) Syst. Control Lett , vol.54 , Issue.11 , pp. 1131-1134
    • de Oliveira, M.1    Geromel, J.2
  • 27
    • 0033325141 scopus 로고    scopus 로고
    • Bi-quadratic stability of uncertain linear systems
    • A. Trofino and C. de Souza, "Bi-quadratic stability of uncertain linear systems," in Proc. IEEE CDC, 1999, pp. 5016-5021.
    • (1999) Proc. IEEE CDC , pp. 5016-5021
    • Trofino, A.1    de Souza, C.2
  • 28
    • 0036993458 scopus 로고    scopus 로고
    • Nonconservative LMI approach to robust stability for systems with uncertain parameters
    • P. Bliman, "Nonconservative LMI approach to robust stability for systems with uncertain parameters," in Proc. IEEE CDC, 2002, pp. 305-310.
    • (2002) Proc. IEEE CDC , pp. 305-310
    • Bliman, P.1
  • 29
    • 1542380049 scopus 로고    scopus 로고
    • Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functions
    • G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functions," in Proc. IEEE CDC, 2003, pp. 4670-4675.
    • (2003) Proc. IEEE CDC , pp. 4670-4675
    • Chesi, G.1    Garulli, A.2    Tesi, A.3    Vicino, A.4
  • 30
    • 16244419436 scopus 로고    scopus 로고
    • Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach
    • Mar
    • G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach," IEEE Trans. Autom. Control, vol. 50, no. 3, pp. 365-370, Mar. 2005.
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.3 , pp. 365-370
    • Chesi, G.1    Garulli, A.2    Tesi, A.3    Vicino, A.4
  • 31
    • 28444472732 scopus 로고    scopus 로고
    • LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions
    • M. de Oliveira and P. Peres, "LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions," Syst. Control Lett., vol. 55, no. 1, pp. 52-61, 2006.
    • (2006) Syst. Control Lett , vol.55 , Issue.1 , pp. 52-61
    • de Oliveira, M.1    Peres, P.2
  • 32
    • 0032255609 scopus 로고    scopus 로고
    • Robust stability analysis for parameter dependent systems using full-block S-procedure
    • M. Dettori and C. Scherer, "Robust stability analysis for parameter dependent systems using full-block S-procedure," in Proc. IEEE CDC 1998, pp. 2798-2799.
    • (1998) Proc. IEEE CDC , pp. 2798-2799
    • Dettori, M.1    Scherer, C.2
  • 33
    • 0034443234 scopus 로고    scopus 로고
    • New robust stability and performance conditions based on parameter dependent multipliers
    • M. Dettori and C. Scherer, "New robust stability and performance conditions based on parameter dependent multipliers," in Proc. IEEE CDC, 2000, pp. 4187-4192.
    • (2000) Proc. IEEE CDC , pp. 4187-4192
    • Dettori, M.1    Scherer, C.2
  • 34
    • 14344257458 scopus 로고    scopus 로고
    • On parameter-dependent Lyapunov functions for robust stability of linear systems
    • D. Henrion, D. Arzelier, D. Peaucelle, and J. Lasserre, "On parameter-dependent Lyapunov functions for robust stability of linear systems," in Proc. IEEE CDC, 2004, pp. 887-892.
    • (2004) Proc. IEEE CDC , pp. 887-892
    • Henrion, D.1    Arzelier, D.2    Peaucelle, D.3    Lasserre, J.4
  • 35
    • 1542379885 scopus 로고    scopus 로고
    • Parameter-dependent Lyapunov functions for exact stability analysis of single-parameter dependent LTI systems
    • X. Zhang, P. Tsiotras, and T. Iwasaki, "Parameter-dependent Lyapunov functions for exact stability analysis of single-parameter dependent LTI systems," in Proc. IEEE CDC, 2003, pp. 5168-5173.
    • (2003) Proc. IEEE CDC , pp. 5168-5173
    • Zhang, X.1    Tsiotras, P.2    Iwasaki, T.3
  • 36
    • 0002676302 scopus 로고    scopus 로고
    • On the kalman-yakubovich-popov lemma
    • A. Rantzer, "On the kalman-yakubovich-popov lemma," Syst. Control Lett., vol. 28, no. 1, pp. 7-10, 1996.
    • (1996) Syst. Control Lett , vol.28 , Issue.1 , pp. 7-10
    • Rantzer, A.1
  • 37
    • 0025747144 scopus 로고
    • Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics
    • Jan
    • M. Fan, A. Tits, and J. Doyle, "Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics," IEEE Trans. Autom. Control, vol. 36, no. 1, pp. 25-38, Jan. 1991.
    • (1991) IEEE Trans. Autom. Control , vol.36 , Issue.1 , pp. 25-38
    • Fan, M.1    Tits, A.2    Doyle, J.3
  • 38
    • 0031192978 scopus 로고    scopus 로고
    • A dual formulation of mixed μ and the losslessness of (D,G) scaling
    • Jul
    • G. Meinsma, Y. Shrivastava, and M. Fu, "A dual formulation of mixed μ and the losslessness of (D,G) scaling," IEEE Trans. Autom. Control vol. 42, no. 7, pp. 1032-1036, Jul. 1997.
    • (1997) IEEE Trans. Autom. Control , vol.42 , Issue.7 , pp. 1032-1036
    • Meinsma, G.1    Shrivastava, Y.2    Fu, M.3
  • 39
    • 0031343105 scopus 로고    scopus 로고
    • Robust stability analysis with quadratic separator: Parametric time-varying uncertainty case
    • T. Iwasaki, "Robust stability analysis with quadratic separator: Parametric time-varying uncertainty case," in Proc. IEEE CDC, 1997, pp. 4880-4885.
    • (1997) Proc. IEEE CDC , pp. 4880-4885
    • Iwasaki, T.1
  • 40
    • 0032267982 scopus 로고    scopus 로고
    • LPV system analysis with quadratic separator
    • T. Iwasaki, "LPV system analysis with quadratic separator," in Proc. IEEE CDC, 1998, pp. 3021-3026.
    • (1998) Proc. IEEE CDC , pp. 3021-3026
    • Iwasaki, T.1
  • 41
    • 0032072577 scopus 로고    scopus 로고
    • Well-posedness of feedback systems: Insights into exact robustness analysis and approximate computations
    • May
    • T. Iwasaki and S. Hara, "Well-posedness of feedback systems: Insights into exact robustness analysis and approximate computations," IEEE Trans. Autom. Control, vol. 43, no. 5, pp. 619-630, May 1998.
    • (1998) IEEE Trans. Autom. Control , vol.43 , Issue.5 , pp. 619-630
    • Iwasaki, T.1    Hara, S.2
  • 42
    • 0035418306 scopus 로고    scopus 로고
    • LPV system analysis via quadratic separator for uncertain implicit systems
    • Aug
    • T. Iwasaki and G. Shibata, "LPV system analysis via quadratic separator for uncertain implicit systems," IEEE Trans. Autom. Control, vol. 46, no. 8, pp. 1195-1208, Aug. 2001.
    • (2001) IEEE Trans. Autom. Control , vol.46 , Issue.8 , pp. 1195-1208
    • Iwasaki, T.1    Shibata, G.2
  • 45
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
    • J. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optim. Meth. Softw., pp. 625-653, 1999.
    • (1999) Optim. Meth. Softw , pp. 625-653
    • Sturm, J.1
  • 46
    • 0034539694 scopus 로고    scopus 로고
    • Robust stability and domain of attraction of uncertain non-linear systems
    • A. Trofini, "Robust stability and domain of attraction of uncertain non-linear systems," in Proc. ACC, 2000, pp. 3707-3711.
    • (2000) Proc. ACC , pp. 3707-3711
    • Trofini, A.1
  • 47
    • 4444352916 scopus 로고    scopus 로고
    • Estimating the domain of attraction for uncertain polynomial systems
    • G. Chesi, "Estimating the domain of attraction for uncertain polynomial systems," Automatica, vol. 40, pp. 1981-1986, 2004.
    • (2004) Automatica , vol.40 , pp. 1981-1986
    • Chesi, G.1
  • 48
    • 46449112048 scopus 로고    scopus 로고
    • Nonlinear Control Analysis and Synthesis Using Sum-of-Squares Programming,
    • Ph.D. dissertation, Univ. California, Berkeley
    • W. Tan, "Nonlinear Control Analysis and Synthesis Using Sum-of-Squares Programming," Ph.D. dissertation, Univ. California, Berkeley, 2006.
    • (2006)
    • Tan, W.1
  • 49
    • 46449112172 scopus 로고    scopus 로고
    • Stability analysis and controller synthesis for parameter-dependent polynomial nonlinear systems
    • D. Zhao, J.Wang, E. Poh, and F. Liao, "Stability analysis and controller synthesis for parameter-dependent polynomial nonlinear systems," in Proc. ACC, 2007, pp. 6015-6020.
    • (2007) Proc. ACC , pp. 6015-6020
    • Zhao, D.1    Wang, J.2    Poh, E.3    Liao, F.4
  • 50
    • 1042300599 scopus 로고    scopus 로고
    • An existence result for polynomial solutions of parameter-dependent LMIs
    • P. Bliman, "An existence result for polynomial solutions of parameter-dependent LMIs," Syst. Control Lett., vol. 51, no. 3-4, pp. 165-169, 2004.
    • (2004) Syst. Control Lett , vol.51 , Issue.3-4 , pp. 165-169
    • Bliman, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.