메뉴 건너뛰기




Volumn 54, Issue 5, 2009, Pages 1019-1024

Stability analysis of time-delay systems with incommensurate delays using positive polynomials

Author keywords

Incommensurate delays; Linear programming; Rekasius substitution; Sum of squares; Time delay systems (TDS)

Indexed keywords

ALTERNATIVE ALGORITHMS; INCOMMENSURATE DELAYS; LINEAR TIME-DELAY SYSTEM; MULTIVARIATE POLYNOMIAL; POSITIVE POLYNOMIALS; REKASIUS SUBSTITUTION; STABILITY ANALYSIS; STABILITY CONDITION; SUM OF SQUARES; TIME-DELAY SYSTEMS; TIME-DELAY SYSTEMS (TDS);

EID: 67349243706     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2017147     Document Type: Article
Times cited : (31)

References (43)
  • 1
    • 39649121256 scopus 로고    scopus 로고
    • LMI characterization of robust stability for time-delay systems: Singular perturbation approach
    • San Diego, CA
    • P.-A. Bliman and T. Iwasaki, "LMI characterization of robust stability for time-delay systems: Singular perturbation approach," in Proc. IEEE Conf. Decision Control, San Diego, CA, 2006, pp. 205-210.
    • (2006) Proc. IEEE Conf. Decision Control , pp. 205-210
    • Bliman, P.-A.1    Iwasaki, T.2
  • 3
    • 33644937447 scopus 로고    scopus 로고
    • Pseudospectral differencing methods for characteristic roots of delay differential equations
    • D. Breda, S. Maset, and R. Vermiglio, "Pseudospectral differencing methods for characteristic roots of delay differential equations," SIAM J. Sci. Comput., vol. 27, no. 2, pp. 482-495, 2005.
    • (2005) SIAM J. Sci. Comput , vol.27 , Issue.2 , pp. 482-495
    • Breda, D.1    Maset, S.2    Vermiglio, R.3
  • 5
    • 0032204104 scopus 로고    scopus 로고
    • Delay-dependent robust stabilization of uncertain systems with multiple state delays
    • Nov
    • Y.-Y. Cao, Y.-X. Sun, and C. Cheng, "Delay-dependent robust stabilization of uncertain systems with multiple state delays," IEEE Trans. Automat. Control, vol. 43, no. 11, pp. 1608-1612, Nov. 1998.
    • (1998) IEEE Trans. Automat. Control , vol.43 , Issue.11 , pp. 1608-1612
    • Cao, Y.-Y.1    Sun, Y.-X.2    Cheng, C.3
  • 7
    • 39649121232 scopus 로고    scopus 로고
    • Stability analysis for time-delay systems using Rekasius's substitution and sum of squares
    • San Diego, CA
    • C. Ebenbauer and F. Allgöwer, "Stability analysis for time-delay systems using Rekasius's substitution and sum of squares," in Proc. 45th IEEE Conf. Decision Control, San Diego, CA, 2006, pp. 5376-5381.
    • (2006) Proc. 45th IEEE Conf. Decision Control , pp. 5376-5381
    • Ebenbauer, C.1    Allgöwer, F.2
  • 8
    • 39449126206 scopus 로고    scopus 로고
    • Extended Kronecker summation for cluster treatment of LTI systems with multiple delays
    • A. F. Ergenc, N. Olgac, and H. Fazelinia, "Extended Kronecker summation for cluster treatment of LTI systems with multiple delays," SIAM J. Control Optim., vol. 46, no. 1, pp. 143-155, 2007.
    • (2007) SIAM J. Control Optim , vol.46 , Issue.1 , pp. 143-155
    • Ergenc, A.F.1    Olgac, N.2    Fazelinia, H.3
  • 9
    • 34249050064 scopus 로고    scopus 로고
    • Stability robustness analysis of multiple time-delayed systems using building block concept
    • May
    • H. Fazelinia, R. Sipahi, and N. Olgac, "Stability robustness analysis of multiple time-delayed systems using building block concept," IEEE Trans. Automat. Control, vol. 52, no. 5, pp. 799-810, May 2007.
    • (2007) IEEE Trans. Automat. Control , vol.52 , Issue.5 , pp. 799-810
    • Fazelinia, H.1    Sipahi, R.2    Olgac, N.3
  • 11
    • 39649105629 scopus 로고    scopus 로고
    • Stability of time-delay systems with non-small delay
    • San Diego, CA
    • F. Gouaisbaut and D. Peaucelle, "Stability of time-delay systems with non-small delay," in Proc. IEEE Conf. Decision Control, San Diego, CA, 2006, pp. 840-845.
    • (2006) Proc. IEEE Conf. Decision Control , pp. 840-845
    • Gouaisbaut, F.1    Peaucelle, D.2
  • 12
    • 0141637436 scopus 로고    scopus 로고
    • Refined discretized Lyapunov functional method for systems with multiple delays
    • K. Gu, "Refined discretized Lyapunov functional method for systems with multiple delays," Int. J. Robust Nonlin. Control, vol. 13, no. 11, pp. 1017-1033, 2003.
    • (2003) Int. J. Robust Nonlin. Control , vol.13 , Issue.11 , pp. 1017-1033
    • Gu, K.1
  • 14
    • 24744452843 scopus 로고    scopus 로고
    • On stability crossing curves for general systems with two delays
    • K. Gu, S.-I. Niculescu, and J. Chen, "On stability crossing curves for general systems with two delays," J. Math. Anal. Appl., vol. 311, pp. 231-253, 2005.
    • (2005) J. Math. Anal. Appl , vol.311 , pp. 231-253
    • Gu, K.1    Niculescu, S.-I.2    Chen, J.3
  • 16
  • 18
    • 0021137891 scopus 로고
    • Simplified analytic stability test for systems with commensurate time delays
    • D. Hertz, E. I. Jury, and E. Zeheb, "Simplified analytic stability test for systems with commensurate time delays," Proc. Inst. Elect. Eng. D, vol. 131, pp. 52-56, 1984.
    • (1984) Proc. Inst. Elect. Eng. D , vol.131 , pp. 52-56
    • Hertz, D.1    Jury, E.I.2    Zeheb, E.3
  • 19
    • 79961130762 scopus 로고    scopus 로고
    • Computing the stability region in delay-space of a TDS using polynomial eigenproblems
    • L'Aquila, Italy, CD ROM
    • E. Jarlebring, "Computing the stability region in delay-space of a TDS using polynomial eigenproblems," in Proc. 6th IFAC Workshop Time Delay Syst., L'Aquila, Italy, 2006, [CD ROM].
    • (2006) Proc. 6th IFAC Workshop Time Delay Syst
    • Jarlebring, E.1
  • 20
    • 0022792173 scopus 로고
    • On a stability test for a class of distributed parameter systems with delays
    • Oct
    • E. I. Jury and E. Zeheb, "On a stability test for a class of distributed parameter systems with delays," IEEE Trans. Circuits Syst., vol. CAS-33, no. 10, pp. 1027-1028, Oct. 1986.
    • (1986) IEEE Trans. Circuits Syst , vol.CAS-33 , Issue.10 , pp. 1027-1028
    • Jury, E.I.1    Zeheb, E.2
  • 21
    • 0032648045 scopus 로고    scopus 로고
    • Robust stability of multivariable polynomials, part 1: Small coefficient perturbations
    • V. L. Kharitonov and J. A. Torres-Muñoz, "Robust stability of multivariable polynomials, part 1: Small coefficient perturbations," Multidimen. Syst. Signal Processing, vol. 10, pp. 7-20, 1999.
    • (1999) Multidimen. Syst. Signal Processing , vol.10 , pp. 7-20
    • Kharitonov, V.L.1    Torres-Muñoz, J.A.2
  • 23
    • 0022128343 scopus 로고
    • Comments on a simplified analytical stability test for systems with delay
    • N. MacDonald, "Comments on a simplified analytical stability test for systems with delay," Proc. Inst. Elect. Eng. D, vol. 132, pp. 237-238, 1985.
    • (1985) Proc. Inst. Elect. Eng. D , vol.132 , pp. 237-238
    • MacDonald, N.1
  • 24
    • 0036112514 scopus 로고    scopus 로고
    • Dynamical systems with multiple time-varying delays: Stability and stabilizability
    • D. Mehdi, E. K. Boukas, and Z. K. Liu, "Dynamical systems with multiple time-varying delays: Stability and stabilizability," J. Optim. Theory Appl., vol. 113, no. 3, pp. 537-565, 2002.
    • (2002) J. Optim. Theory Appl , vol.113 , Issue.3 , pp. 537-565
    • Mehdi, D.1    Boukas, E.K.2    Liu, Z.K.3
  • 26
    • 46449102412 scopus 로고    scopus 로고
    • Stability of networked systems with multiple delays using linear programming
    • New York, NY
    • U. Münz, C. Ebenbauer, and F. Allgöwer, "Stability of networked systems with multiple delays using linear programming," in Proc. Amer. Control Conf., New York, NY, 2007, pp. 5515-5520.
    • (2007) Proc. Amer. Control Conf , pp. 5515-5520
    • Münz, U.1    Ebenbauer, C.2    Allgöwer, F.3
  • 28
    • 0032074234 scopus 로고    scopus 로고
    • Robust exponential stability of uncertain systems with time-varying delays
    • May
    • S.-I. Niculescu, C. E. Souza, L. Dugard, and J.-M. Dion, "Robust exponential stability of uncertain systems with time-varying delays," IEEE Trans. Automat. Control, vol. 43, no. 5, pp. 743-748, May 1998.
    • (1998) IEEE Trans. Automat. Control , vol.43 , Issue.5 , pp. 743-748
    • Niculescu, S.-I.1    Souza, C.E.2    Dugard, L.3    Dion, J.-M.4
  • 29
    • 0003406070 scopus 로고    scopus 로고
    • Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization,
    • Ph.D. dissertation, California Institute of Technology, Pasadena
    • P. A. Parrilo, "Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization," Ph.D. dissertation, California Institute of Technology, Pasadena, 2000.
    • (2000)
    • Parrilo, P.A.1
  • 30
    • 33947713030 scopus 로고    scopus 로고
    • Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation
    • D. Peaucelle, D. Arzelier, D. Henrion, and F. Gouaisbaut, "Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation," Automatica, vol. 43, no. 5, pp. 795-804, 2007.
    • (2007) Automatica , vol.43 , Issue.5 , pp. 795-804
    • Peaucelle, D.1    Arzelier, D.2    Henrion, D.3    Gouaisbaut, F.4
  • 31
    • 67349135406 scopus 로고    scopus 로고
    • Positive forms and stability of linear time-delay systems
    • M. Peet, A. Papachristodoulou, and S. Lall, "Positive forms and stability of linear time-delay systems," SIAM J. Control Optim., vol. 47, no. 6, pp. 3237-3258, 2009.
    • (2009) SIAM J. Control Optim , vol.47 , Issue.6 , pp. 3237-3258
    • Peet, M.1    Papachristodoulou, A.2    Lall, S.3
  • 33
    • 0032064831 scopus 로고    scopus 로고
    • An algorithm for sums of squares of real polynomials
    • V. Powers and T. Wörmann, "An algorithm for sums of squares of real polynomials," J. Pure Appl. Algebra, vol. 127, pp. 99-104, 1998.
    • (1998) J. Pure Appl. Algebra , vol.127 , pp. 99-104
    • Powers, V.1    Wörmann, T.2
  • 36
    • 0009617924 scopus 로고
    • A stability test for systems with delays
    • San Francisco, CA, CD ROM
    • Z. V. Rekasius, "A stability test for systems with delays," in Proc. Joint Automat. Control Conf., San Francisco, CA, 1980, [CD ROM].
    • (1980) Proc. Joint Automat. Control Conf
    • Rekasius, Z.V.1
  • 37
    • 0001157581 scopus 로고    scopus 로고
    • Some concrete aspects of Hilbert's 17th problem
    • B. Reznick, "Some concrete aspects of Hilbert's 17th problem," Contemp. Math., vol. 253, pp. 251-272, 2000.
    • (2000) Contemp. Math , vol.253 , pp. 251-272
    • Reznick, B.1
  • 38
    • 0033296299 scopus 로고    scopus 로고
    • Using SeDuMi 1.02, aMATLAB toolbox for optimization over symmetric cones
    • J. F. Sturm, "Using SeDuMi 1.02, aMATLAB toolbox for optimization over symmetric cones," Optim. Methods Software, vol. 11, no. 1-4, pp. 625-653, 1999.
    • (1999) Optim. Methods Software , vol.11 , Issue.1-4 , pp. 625-653
    • Sturm, J.F.1
  • 39
    • 0030785257 scopus 로고    scopus 로고
    • On the stability of uncertain systems with multiple time-varying delays
    • Jan
    • Y.-J. Sun, J.-G. Hsieh, and H.-C. Yang, "On the stability of uncertain systems with multiple time-varying delays," IEEE Trans. Automat. Control, vol. 42, no. 1, pp. 101-105, Jan 1997.
    • (1997) IEEE Trans. Automat. Control , vol.42 , Issue.1 , pp. 101-105
    • Sun, Y.-J.1    Hsieh, J.-G.2    Yang, H.-C.3
  • 40
    • 0008144734 scopus 로고
    • An analytical stability test for a class of time-delay systems
    • Jun
    • A. Thowsen, "An analytical stability test for a class of time-delay systems," IEEE Trans. Automat. Control, vol. AC-26, no. 3, pp. 735-736, Jun. 1981.
    • (1981) IEEE Trans. Automat. Control , vol.AC-26 , Issue.3 , pp. 735-736
    • Thowsen, A.1
  • 41
    • 0037396259 scopus 로고    scopus 로고
    • Delay-dependent/delay-independent stability of linear systems with multiple time-varying delays
    • Apr
    • B. Xu and Y.-H. Liu, "Delay-dependent/delay-independent stability of linear systems with multiple time-varying delays," IEEE Trans. Automat. Control, vol. 48, no. 4, pp. 697-701, Apr. 2003.
    • (2003) IEEE Trans. Automat. Control , vol.48 , Issue.4 , pp. 697-701
    • Xu, B.1    Liu, Y.-H.2
  • 42
    • 0142027787 scopus 로고    scopus 로고
    • New results for the analysis of linear systems with time-invariant delays
    • J. Zhang, C. R. Knospe, and P. Tsiotras, "New results for the analysis of linear systems with time-invariant delays," Int. J. Robust Nonlin. Control, vol. 13, no. 12, pp. 1149-1175, 2003.
    • (2003) Int. J. Robust Nonlin. Control , vol.13 , Issue.12 , pp. 1149-1175
    • Zhang, J.1    Knospe, C.R.2    Tsiotras, P.3
  • 43
    • 0030360422 scopus 로고    scopus 로고
    • Complexity issues in robust stability of linear differential systems
    • O. Toker and H. Ozbay, "Complexity issues in robust stability of linear differential systems," Math. Control, Signals, Syst., vol. 9, no. 4, pp. 386-400, 1996.
    • (1996) Math. Control, Signals, Syst , vol.9 , Issue.4 , pp. 386-400
    • Toker, O.1    Ozbay, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.