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Volumn 48, Issue 8, 2010, Pages 5564-5582

An eigenvalue perturbation approach to stability analysis, Part I: Eigenvalue series of matrix operators

Author keywords

Asymptotic analysis; Eigenvalue series; Matrix perturbation; Stability; Time delay systems

Indexed keywords

ASYMPTOTIC BEHAVIORS; COMPUTATIONAL SOLUTIONS; DELAY SYSTEMS; EIGEN-VALUE; EIGENVALUE PERTURBATION; HALF-PLANES; HOLOMORPHIC MATRIX; LINEAR TIME-INVARIANT; MATHEMATICAL TOOLS; MATRIX; MATRIX PERTURBATION; PARAMETER VARIATION; STABILITY ANALYSIS; SYSTEMS ANALYSIS AND DESIGN; TIME-DELAY SYSTEMS;

EID: 79251495436     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/080741707     Document Type: Article
Times cited : (48)

References (25)
  • 2
    • 0036568247 scopus 로고    scopus 로고
    • Limiting zero distribution of sampled systems
    • E. W. BAI AND Y. Q. WU, Limiting zero distribution of sampled systems, Automatica, 38 (2002), pp. 843-851.
    • (2002) Automatica , vol.38 , pp. 843-851
    • Bai, E.W.1    Wu, Q.Y.2
  • 3
    • 0032672448 scopus 로고    scopus 로고
    • On zeros of pulse transfer functions
    • M. J. BLACHUTA, On zeros of pulse transfer functions, IEEE Trans. Automat. Control, 44 (1999), pp. 1229-1234.
    • (1999) IEEE Trans. Automat. Control , vol.44 , pp. 1229-1234
    • Blachuta, M.J.1
  • 5
    • 0004843041 scopus 로고
    • Static output feedback stabilization for SISO systems and related problems: Solutions via generalized eigenvalues
    • J. CHEN, Static output feedback stabilization for SISO systems and related problems: Solutions via generalized eigenvalues, Control Theory Adv. Tech., 10 (1995), pp. 2233-2244.
    • (1995) Control Theory Adv. Tech. , vol.10 , pp. 2233-2244
    • Chen, J.1
  • 8
    • 79251502951 scopus 로고    scopus 로고
    • An eigenvalue perturbation approach to stability analysis, Part II: When will zeros of time-delay systems cross imaginary axis?
    • J. CHEN, P. FU, S.-I. NLCULESCU, AND Z. GUAN, An eigenvalue perturbation approach to stability analysis, Part II: When will zeros of time-delay systems cross imaginary axis?, SIAM J. Control Optim., 48 (2010), pp. 5583-5605.
    • (2010) SIAM J. Control Optim. , vol.48 , pp. 5583-5605
    • Chen, J.1    Fu, P.2    Nlculescu, S.-I.3    Guan, Z.4
  • 9
    • 0003853433 scopus 로고
    • Abacus Press, Tunbridge Wells, UK; Halstead Press [John Wiley & Sons, Inc.], New York
    • A. S. DEIF, Advanced Matrix Theory for Scientists and Engineers, Abacus Press, Tunbridge Wells, UK; Halstead Press [John Wiley & Sons, Inc.], New York, 1982.
    • (1982) Advanced Matrix Theory for Scientists and Engineers
    • Deif, A.S.1
  • 11
    • 0030086463 scopus 로고    scopus 로고
    • Analytic study on the intrinsic zeros of sampled-data systems
    • T. HAGIWARA, Analytic study on the intrinsic zeros of sampled-data systems, IEEE Trans. Automat. Control, 41 (1996), pp. 261-263.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 261-263
    • Hagiwara, T.1
  • 12
    • 0024082715 scopus 로고
    • Maximal unidirectional perturbation bounds for stability of polynomials and matrices
    • M. FU and B. R. BARMISH, Maximal unidirectional perturbation bounds for stability of polynomials and matrices, Systems Control Lett., 11 (1988), pp. 173-179.
    • (1988) Systems Control Lett. , vol.11 , pp. 173-179
    • Fu, M.1    Barmish, B.R.2
  • 13
    • 0000114729 scopus 로고
    • Hermitian pencils and output feedback stabilization of scalar systems
    • U. HELMKE AND B. D. O. ANDERSON, Hermitian pencils and output feedback stabilization of scalar systems, Int. J. Control, 56 (1992), pp. 857-876.
    • (1992) Int. J. Control , vol.56 , pp. 857-876
    • Helmke, U.1    Anderson, B.D.O.2
  • 15
    • 0009299728 scopus 로고
    • Remarks on the perturbation of analytic matrix functions. III
    • H. LANGER AND B. NAJMAN, Remarks on the perturbation of analytic matrix functions. III, Integral Equations Operator Theory, 15 (1992), pp. 796-806.
    • (1992) Integral Equations Operator Theory , vol.15 , pp. 796-806
    • Langer, H.1    Najman, B.2
  • 17
    • 33746074803 scopus 로고    scopus 로고
    • An exact stability analysis test for single-parameter polynomially-dependent linear systems
    • P. TSIOTRAS AND P. A. BLIMAN, An exact stability analysis test for single-parameter polynomially-dependent linear systems, IEEE Trans. Automat. Control, 51 (2006), pp. 1161-1164.
    • (2006) IEEE Trans. Automat. Control , vol.51 , pp. 1161-1164
    • Tsiotras, P.1    Bliman, P.A.2
  • 18
    • 33746077055 scopus 로고    scopus 로고
    • On the degree of polynomial parameter-dependent Lyapunov functions for robust stability of single parameter-dependent LTI systems: A counterexample to Barmish's conjecture
    • Y. EBIHARA AND T. HAGIWARA, On the degree of polynomial parameter-dependent Lyapunov functions for robust stability of single parameter-dependent LTI systems: A counterexample to Barmish's conjecture, Automatica, 42 (2005), pp. 1599-1603.
    • (2005) Automatica , vol.42 , pp. 1599-1603
    • Ebihara, Y.1    Hagiwara, T.2
  • 19
    • 1542379885 scopus 로고    scopus 로고
    • Parameter-dependent Lyapunov functions for exact stability analysis of single-parameter dependent LTI systems
    • Maui, HI
    • X. ZHANG, P. TSIOTRAS, AND T. IWASAKI, Parameter-dependent Lyapunov functions for exact stability analysis of single-parameter dependent LTI systems, in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, 2003, pp. 5168-5173.
    • (2003) Proceedings of the 42nd IEEE Conference on Decision and Control , pp. 5168-5173
    • Zhang, X.1    Tsiotras, P.2    Iwasaki, T.3
  • 22
    • 0010437249 scopus 로고
    • A note on local behavior of multiple eigenvalues
    • J.-G. SUN, A note on local behavior of multiple eigenvalues, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 533-541.
    • (1989) SIAM J. Matrix Anal. Appl. , vol.10 , pp. 533-541
    • Sun, J.-G.1
  • 24
    • 0141732284 scopus 로고    scopus 로고
    • On the sensitivity of multiple eigenvalues of nonsymmetric matrix pencils
    • H. XIE AND H. DAI, On the sensitivity of multiple eigenvalues of nonsymmetric matrix pencils, Linear Algebra Appl., 374 (2003), pp. 143-158.
    • (2003) Linear Algebra Appl. , vol.374 , pp. 143-158
    • Xie, H.1    Dai, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.