메뉴 건너뛰기




Volumn 349, Issue 1-3, 2002, Pages 155-185

Numerical solution and perturbation theory for generalized Lyapunov equations

Author keywords

Condition numbers; Deflating subspaces; Generalized Lyapunov equations; Matrix pencils; Perturbation theory; Spectral projections

Indexed keywords

CONTINUOUS TIME SYSTEMS; LYAPUNOV FUNCTIONS; MATRIX ALGEBRA; NUMBER THEORY;

EID: 31244438168     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(02)00255-0     Document Type: Article
Times cited : (41)

References (45)
  • 2
    • 84976855597 scopus 로고
    • Solution of the equation AX+XB=C
    • R.H. Bartels, and G.W. Stewart Solution of the equation AX+XB=C Comm. ACM 15 9 1972 820 826
    • (1972) Comm. ACM , vol.15 , Issue.9 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 3
    • 0003100869 scopus 로고
    • An improved algorithm for the computation of Knonecker's canonical form of a singular pencil
    • T. Beelen, and P. Van Dooren An improved algorithm for the computation of Knonecker's canonical form of a singular pencil Linear Algebra Appl. 105 1988 9 65
    • (1988) Linear Algebra Appl. , vol.105 , pp. 9-65
    • Beelen, T.1    Van Dooren, P.2
  • 4
    • 0023328005 scopus 로고
    • Lyapunov-like equations and reachability/observability Gramians for descriptor systems
    • D.J. Bender Lyapunov-like equations and reachability/observability Gramians for descriptor systems IEEE Trans. Automat. Control 32 4 1987 343 348
    • (1987) IEEE Trans. Automat. Control , vol.32 , Issue.4 , pp. 343-348
    • Bender, D.J.1
  • 6
    • 0033412866 scopus 로고    scopus 로고
    • Solving stable generalized Lyapunov equations with the matrix sign function
    • P. Benner, and E.S. Quintana-Ort Solving stable generalized Lyapunov equations with the matrix sign function Numer. Algorithms 20 1 1999 75 100
    • (1999) Numer. Algorithms , vol.20 , Issue.1 , pp. 75-100
    • Benner, P.1    Quintana-Ort, E.S.2
  • 7
    • 4644340124 scopus 로고
    • On the stability radius of a generlized state-space system
    • R. Byers, and N.K. Nichols On the stability radius of a generlized state-space system Linear Algebra Appl. 188/189 1993 113 134
    • (1993) Linear Algebra Appl. , vol.188-189 , pp. 113-134
    • Byers, R.1    Nichols, N.K.2
  • 9
    • 38149012697 scopus 로고
    • ThesolutionofthematrixequationsAXB-CXD=Eand(YA-DZ,YC-BZ)=(E,F)
    • K.E. Chu ThesolutionofthematrixequationsAXB-CXD=Eand(YA-DZ,YC-BZ)=(E,F) Linear Algebra Appl. 93 1987 93 105
    • (1987) Linear Algebra Appl. , vol.93 , pp. 93-105
    • Chu, K.E.1
  • 10
    • 45949117656 scopus 로고
    • Computing stable eigendecompositions of matrix pencils
    • J.W. Demmel, and B. Kågström Computing stable eigendecompositions of matrix pencils Linear Algebra Appl. 88/89 1987 139 186
    • (1987) Linear Algebra Appl. , vol.88-89 , pp. 139-186
    • Demmel, J.W.1    Kågström, B.2
  • 11
    • 0027608731 scopus 로고
    • The generalized Schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applicaitons. Part I: Theory and algorithms
    • J.W. Demmel, and B. Kågström The generalized Schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applicaitons. Part I: Theory and algorithms ACM Trans. Math. Software 19 2 1993 160 174
    • (1993) ACM Trans. Math. Software , vol.19 , Issue.2 , pp. 160-174
    • Demmel, J.W.1    Kågström, B.2
  • 12
    • 0027609950 scopus 로고
    • The generalized Schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applications. Part II: Software and applications
    • J.W. Demmel, and B. Kågström The generalized Schur decomposition of an arbitrary pencil A-λB: Robust software with error bounds and applications. Part II: Software and applications ACM Trans. Math. Software 19 2 1993 175 201
    • (1993) ACM Trans. Math. Software , vol.19 , Issue.2 , pp. 175-201
    • Demmel, J.W.1    Kågström, B.2
  • 15
    • 0026877146 scopus 로고
    • Algorithm 705: A Fortran-77 software package for solving the Sylvester matrix equation AXBT+CXDT=E
    • J.D. Gardiner, M.R. Wette, A.J. Laub, J.J. Amato, and C.B. Moler Algorithm 705: A Fortran-77 software package for solving the Sylvester matrix equation AXBT+CXDT=E ACM Trans. Math. Software 18 2 1992 232 238
    • (1992) ACM Trans. Math. Software , vol.18 , Issue.2 , pp. 232-238
    • Gardiner, J.D.1    Wette, M.R.2    Laub, A.J.3    Amato, J.J.4    Moler, C.B.5
  • 17
    • 0004236492 scopus 로고    scopus 로고
    • third ed. The Johns Hopkins University Press Baltimore, London
    • G.H. Golub, and C.F. Van Loan Matrix Computations third ed. 1996 The Johns Hopkins University Press Baltimore, London
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 19
    • 0000567621 scopus 로고
    • Numerical solution of the stable non-negative definite Lyapunov equation
    • S.J. Hammarling Numerical solution of the stable non-negative definite Lyapunov equation IMA J. Numer. Anal. 2 1982 303 323
    • (1982) IMA J. Numer. Anal. , vol.2 , pp. 303-323
    • Hammarling, S.J.1
  • 20
    • 0023966821 scopus 로고
    • The sensitivity of the stable Lyapunov equation
    • G. Hewer, and C. Kenney The sensitivity of the stable Lyapunov equation SIAM J. Control Optim. 26 2 1988 321 344
    • (1988) SIAM J. Control Optim. , vol.26 , Issue.2 , pp. 321-344
    • Hewer, G.1    Kenney, C.2
  • 24
    • 21844500600 scopus 로고
    • A perturbation analysis of the generalized Sylvester equation (AR-LB,DR-LE)=(C,F)
    • B. Kågström A perturbation analysis of the generalized Sylvester equation (AR-LB,DR-LE)=(C,F) SIAM J. Matrix Anal. Appl. 15 4 1994 1045 1060
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , Issue.4 , pp. 1045-1060
    • Kågström, B.1
  • 25
    • 0041103179 scopus 로고    scopus 로고
    • Computing eigenspaces with specified eigenvalues of a regular matrix pencil (A,B) and conditon estimation: Theory, algorithms and software
    • B. Kågström, and P. Poromaa Computing eigenspaces with specified eigenvalues of a regular matrix pencil (A,B) and conditon estimation: theory, algorithms and software Numer. Algorithms 12 1996 369 407
    • (1996) Numer. Algorithms , vol.12 , pp. 369-407
    • Kågström, B.1    Poromaa, P.2
  • 26
    • 0030092417 scopus 로고    scopus 로고
    • LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs
    • B. Kågström, and P. Poromaa LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs ACM Trans. Math. Software 22 1 1996 78 103
    • (1996) ACM Trans. Math. Software , vol.22 , Issue.1 , pp. 78-103
    • Kågström, B.1    Poromaa, P.2
  • 27
    • 0024700168 scopus 로고
    • Generalized Schur methods with condition estimators for solving the generalized Sylvester equation
    • B. Kågström, and L. Westin Generalized Schur methods with condition estimators for solving the generalized Sylvester equation IEEE Trans. Automat. Control 34 1989 745 751
    • (1989) IEEE Trans. Automat. Control , vol.34 , pp. 745-751
    • Kågström, B.1    Westin, L.2
  • 35
    • 0007065244 scopus 로고
    • Construction of a solution of the generalized Lyapunov equation
    • V.B. Larin Construction of a solution of the generalized Lyapunov equation Russian Acad. Sci., Dokl., Math. 47 1 1993 17 20
    • (1993) Russian Acad. Sci., Dokl., Math. , vol.47 , Issue.1 , pp. 17-20
    • Larin, V.B.1
  • 36
    • 0023288081 scopus 로고
    • Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
    • A.J. Laub, M.T. Heath, C.C. Paige, and R.C. Ward Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms IEEE Trans. Automat. Control AC-32 2 1987 115 122
    • (1987) IEEE Trans. Automat. Control , vol.32 AC- , Issue.2 , pp. 115-122
    • Laub, A.J.1    Heath, M.T.2    Paige, C.C.3    Ward, R.C.4
  • 38
    • 84983759108 scopus 로고
    • Stability of linear mechanical systems with holonomic constraints
    • P.C. Müller Stability of linear mechanical systems with holonomic constraints Appl. Mech. Rev. 46 11 1993 160 164
    • (1993) Appl. Mech. Rev. , vol.46 , Issue.11 , pp. 160-164
    • Müller, P.C.1
  • 39
    • 0032342953 scopus 로고    scopus 로고
    • Numerical solution of generalized Lyapunov equations
    • T. Penzl Numerical solution of generalized Lyapunov equations Adv. Comput. Math. 8 1-2 1998 33 48
    • (1998) Adv. Comput. Math. , vol.8 , Issue.1-2 , pp. 33-48
    • Penzl, T.1
  • 40
    • 0001162599 scopus 로고
    • Error and perturbation bounds for subspaces associated wth certain eigenvalue problems
    • G.W. Stewart Error and perturbation bounds for subspaces associated wth certain eigenvalue problems SIAM Rev. 15 1973 727 764
    • (1973) SIAM Rev. , vol.15 , pp. 727-764
    • Stewart, G.W.1
  • 42
    • 1642268497 scopus 로고    scopus 로고
    • On criteria for asymptotic stability of differential-algebraic equations
    • T. Stykel On criteria for asymptotic stability of differential-algebraic equations Z. Angew. Math. Mech. 82 3 2002 147 158
    • (2002) Z. Angew. Math. Mech. , vol.82 , Issue.3 , pp. 147-158
    • Stykel, T.1
  • 43
    • 0011860416 scopus 로고    scopus 로고
    • Preprint SFB393/00-38, Fakultät für Mathematik, Technische Universität Chemnitz, D- 09107 Chemnitz, Germany, October
    • T. Stykel, Generalized Lyapunov equations for descriptor systems: stability and inertia theorems (submitted). Preprint SFB393/00-38, Fakultät für Mathematik, Technische Universität Chemnitz, D- 09107 Chemnitz, Germany, October 2000. Available from http: //www.tu-chemnitz.de/sfb393/sfb00pr.html
    • (2000) Generalized Lyapunov Equations for Descriptor Systems: Stability and Inertia Theorems (Submitted)
    • Stykel, T.1
  • 44
    • 0000769280 scopus 로고
    • The computation of the Kronecker's canonical form of a singular pencil
    • P. Van Dooren The computation of the Kronecker's canonical form of a singular pencil Linear Algebra Appl. 27 1979 103 140
    • (1979) Linear Algebra Appl. , vol.27 , pp. 103-140
    • Van Dooren, P.1
  • 45
    • 0041911280 scopus 로고    scopus 로고
    • Performance of the QZ algorithm in the presence of infinite eigenvalues
    • D.S. Watkins Performance of the QZ algorithm in the presence of infinite eigenvalues SIAM J. Matrix Anal. Appl. 22 2 2000 364 375
    • (2000) SIAM J. Matrix Anal. Appl. , vol.22 , Issue.2 , pp. 364-375
    • Watkins, D.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.