메뉴 건너뛰기




Volumn 45, Issue 3, 2006, Pages 856-884

Interconnected systems with uncertain couplings: Explicit formulae for μ-values, spectral value sets, and stability radii

Author keywords

values; Linear systems; Perturbations; Spectral value sets; Stability radii

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; PERTURBATION TECHNIQUES; SET THEORY; THEOREM PROVING;

EID: 34249052261     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/050626508     Document Type: Article
Times cited : (24)

References (29)
  • 3
    • 0040170911 scopus 로고
    • Limits for the characteristic roots of a matrix
    • A. BRAUER, Limits for the characteristic roots of a matrix. II, Duke Math. J., 14 (1947), pp. 21-26.
    • (1947) II, Duke Math. J , vol.14 , pp. 21-26
    • BRAUER, A.1
  • 4
    • 0039579464 scopus 로고
    • Matrices, eigenvalues, and directed graphs
    • R. A. BRUALDI, Matrices, eigenvalues, and directed graphs, Linear and Multilinear Algebra, 11 (1982), pp. 143-165.
    • (1982) Linear and Multilinear Algebra , vol.11 , pp. 143-165
    • BRUALDI, R.A.1
  • 6
    • 0030257679 scopus 로고    scopus 로고
    • Structured singular values with nondiagonal structures. I. Characterizations; Part II. Computation
    • M. J. CHEN, K. N. FAN, AND C. N. NETT, Structured singular values with nondiagonal structures. I. Characterizations; Part II. Computation, IEEE Trans. Automat. Control, 41 (1996), pp. 1507-1516.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 1507-1516
    • CHEN, M.J.1    FAN, K.N.2    NETT, C.N.3
  • 7
    • 0020203138 scopus 로고
    • Analysis of feedback systems with structured uncertainties
    • J. C. DOYLE, Analysis of feedback systems with structured uncertainties, Proc. IEE-D, 129 (1982), pp. 242-250.
    • (1982) Proc. IEE-D , vol.129 , pp. 242-250
    • DOYLE, J.C.1
  • 9
    • 0008852960 scopus 로고    scopus 로고
    • Computing spectral value sets using the subharmonicity of the norm of rational matrices
    • E. GALLESTEY, Computing spectral value sets using the subharmonicity of the norm of rational matrices, BIT, 38 (1998), pp. 22-33.
    • (1998) BIT , vol.38 , pp. 22-33
    • GALLESTEY, E.1
  • 11
    • 0034144755 scopus 로고    scopus 로고
    • A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra
    • N. J. HIGHAM AND F. TISSEUR, A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra, SIAM J. Matrix Anal. Appl., 21 (2000), pp. 1185-1201.
    • (2000) SIAM J. Matrix Anal. Appl , vol.21 , pp. 1185-1201
    • HIGHAM, N.J.1    TISSEUR, F.2
  • 12
    • 0027642197 scopus 로고
    • Spectral value sets: A graphical tool for robustness analysis
    • D. HINRICHSEN AND B. KELB, Spectral value sets: A graphical tool for robustness analysis, Systems Control Lett., 21 (1993), pp. 127-136.
    • (1993) Systems Control Lett , vol.21 , pp. 127-136
    • HINRICHSEN, D.1    KELB, B.2
  • 13
    • 0000241112 scopus 로고
    • Real and complex stability radii: A survey
    • D. Hinrichsen and B. Mårtensson, eds, Birkhäuser-Verlag, Basel, Switzerland
    • D. HINRICHSEN AND A. J. PRITCHAR, Real and complex stability radii: A survey, in Control of Uncertain Systems, D. Hinrichsen and B. Mårtensson, eds., Birkhäuser-Verlag, Basel, Switzerland, 1990, pp. 119-162.
    • (1990) Control of Uncertain Systems , pp. 119-162
    • HINRICHSEN, D.1    PRITCHAR, A.J.2
  • 14
    • 11544255503 scopus 로고
    • On the robustness of stable discrete-time linear systems
    • Genoa, Birkhäuser-Verlag, Basel, Switzerland
    • D. HINRICHSEN AND A. J. PRITCHARD, On the robustness of stable discrete-time linear systems, in New Trends in Systems Theory (Genoa, 1990), Birkhäuser-Verlag, Basel, Switzerland, 1991, pp. 393-400.
    • (1990) New Trends in Systems Theory , pp. 393-400
    • HINRICHSEN, D.1    PRITCHARD, A.J.2
  • 16
    • 0004151494 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1990.
    • (1990) Matrix Analysis
    • HORN, R.A.1    JOHNSON, C.R.2
  • 17
    • 4444304758 scopus 로고    scopus 로고
    • Ph.D. thesis, University of Bremen, Bremen, Germany
    • M. KAROW, Geometry of Spectral Value Sets, Ph.D. thesis, University of Bremen, Bremen, Germany, 2003.
    • (2003) Geometry of Spectral Value Sets
    • KAROW, M.1
  • 18
    • 0034159737 scopus 로고    scopus 로고
    • A fast algorithm for the computation of an upper bound on the μ-norm
    • T. C. LAWRENCE, A. L. TITS, AND P. VAN DOOREN, A fast algorithm for the computation of an upper bound on the μ-norm, Automatica, 36 (2000), pp. 449-456.
    • (2000) Automatica , vol.36 , pp. 449-456
    • LAWRENCE, T.C.1    TITS, A.L.2    VAN DOOREN, P.3
  • 19
    • 0027205718 scopus 로고
    • The complex structured singular value
    • A. PACKARD AND J. C. DOYLE, The complex structured singular value, Automatica J. IFAC, 29 (1993), pp. 71-109.
    • (1993) Automatica J. IFAC , vol.29 , pp. 71-109
    • PACKARD, A.1    DOYLE, J.C.2
  • 20
    • 0029766067 scopus 로고    scopus 로고
    • On the robustness of symmetric systems
    • L. QIU, On the robustness of symmetric systems, Systems Control Lett., 27 (1996), pp. 187-190.
    • (1996) Systems Control Lett , vol.27 , pp. 187-190
    • QIU, L.1
  • 23
    • 0018205688 scopus 로고
    • Tight bounds on the response of multivariable systems with component uncertainty
    • University of Illinois, Urbana, IL
    • M. G. SAFONOV. Tight bounds on the response of multivariable systems with component uncertainty, in 16th Annual Allerton Conference on Communication, Control, and Computing, University of Illinois, Urbana, IL, 1978, pp. 451-460.
    • (1978) 16th Annual Allerton Conference on Communication, Control, and Computing , pp. 451-460
    • SAFONOV, M.G.1
  • 25
    • 0003748014 scopus 로고
    • Large Scale Dynamic Systems. Stability and Structure
    • Engrg, North-Holland, New York
    • D.D. ŠILJAK, Large Scale Dynamic Systems. Stability and Structure, North-Holland Ser. System Sci. Engrg., North-Holland, New York, 1978.
    • (1978) North-Holland Ser. System Sci
    • ŠILJAK, D.D.1
  • 26
    • 85011519633 scopus 로고    scopus 로고
    • Computation of pseudospectra
    • L. N. TREFETHEN, Computation of pseudospectra, Acta Numer., 8 (1999), pp. 247-295.
    • (1999) Acta Numer , vol.8 , pp. 247-295
    • TREFETHEN, L.N.1
  • 28
    • 3042552171 scopus 로고    scopus 로고
    • Geršgorin-type eigenvalue inclusion theorems and their sharpness
    • R. S. VARGA, Geršgorin-type eigenvalue inclusion theorems and their sharpness, Electron. Trans. Numer. Anal., 12 (2001), pp. 113-133.
    • (2001) Electron. Trans. Numer. Anal , vol.12 , pp. 113-133
    • VARGA, R.S.1
  • 29
    • 34047098116 scopus 로고    scopus 로고
    • Geršgorin and His Circles
    • Springer-Verlag, Berlin
    • R. S. VARGA, Geršgorin and His Circles, Springer Ser. Comput. Math. 36, Springer-Verlag, Berlin, 2004.
    • (2004) Springer Ser. Comput. Math , vol.36
    • VARGA, R.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.