The quadratic eigenvalue problem in electric power systems

The application of the quadratic eigenvalue problem in electrical power systems is reviewed. The spectrum and pseudospectrum of an electrical power system are defined.

[1]  Christian Commault,et al.  Structure of linear systems: Geometric and transfer matrix approaches , 1991, Kybernetika.

[2]  L. Trefethen,et al.  Eigenvalues and Pseudospectra of Rectangular Matrices , 2001 .

[3]  L. Trefethen.  Approximation theory and numerical linear algebra , 1990 .

[4]  Lloyd N. Trefethen,et al.  Generalizing Eigenvalue Theorems to Pseudospectra Theorems , 2001, SIAM J. Sci. Comput..

[5]  H. Rosenbrock,et al.  State-space and multivariable theory, , 1970 .

[6]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[7]  Lloyd N. Trefethen,et al.  Computation of pseudospectra , 1999, Acta Numerica.

[8]  Boris T. Polyak.  Robust Linear Algebra and Robust Aperiodicity , 2003 .

[9]  James Demmel,et al.  Applied Numerical Linear Algebra , 1997 .

[10]  E. Kamke.  Differentialgleichungen : Lösungsmethoden und Lösungen , 1977 .

[11]  Françoise Tisseur,et al.  A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems , 2002, SIAM J. Matrix Anal. Appl..

[12]  Efstratios Gallopoulos,et al.  TRANSFER FUNCTIONS AND RESOLVENT NORM APPROXIMATION OF LARGE MATRICES , 1998 .

[13]  H. H. Rosenbrock,et al.  Dynamical indices of a transfer function matrix , 1974 .

[14]  Gene H. Golub,et al.  Matrix computations , 1983 .

[15]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[16]  P. Kundur,et al.  Power system stability and control , 1994 .

[17]  J. Varah.  On the Separation of Two Matrices , 1979 .

[18]  F. Tisseur.  Backward error and condition of polynomial eigenvalue problems , 2000 .

[19]  Lloyd N. Trefethen,et al.  Pseudospectra of Linear Operators , 1997, SIAM Rev..

[20]  H. Rosenbrock.  Structural properties of linear dynamical systems , 1974 .

[21]  Karl Meerbergen,et al.  The Quadratic Eigenvalue Problem , 2001, SIAM Rev..

[22]  M. N. Spijker,et al.  Linear stability analysis in the numerical solution of initial value problems , 1993, Acta Numerica.

[23]  C. T. Fike,et al.  Norms and exclusion theorems , 1960 .

[24]  Tosio Kato.  Perturbation theory for linear operators , 1966 .