|
[1]
|
N. Aliyev, P. Benner, E. Mengi, P. Schwerdtner and M. Voigt, Large-scale computation of $\mathcal{L}_∞$-norms by a greedy subspace method,
SIAM J. Matrix Anal. Appl., Accepted for publication.
|
|
[2]
|
P. Benner, R. Byers, P. Losse, V. Mehrmann and H. Xu, Numerical solution of real skew-Hamiltonian/Hamiltonian eigenproblems, 2007, Unpublished report.
|
|
[3]
|
P. Benner, R. Byers, V. Mehrmann and H. Xu, Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils, SIAM J. Matrix Anal. Appl., 24 (2002), 165-190.
doi: 10.1137/S0895479800367439.
|
|
[4]
|
P. Benner and C. Effenberger, A rational SHIRA method for the Hamiltonian eigenvalue problem, Taiwanese J. Math., 14 (2010), 805-823.
doi: 10.11650/twjm/1500405868.
|
|
[5]
|
P. Benner and H. Faßbender, An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem, Linear Algebra Appl., 263 (1997), 75-111.
doi: 10.1016/S0024-3795(96)00524-1.
|
|
[6]
|
P. Benner, H. Faßbender and M. Stoll, A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process, Linear Algebra Appl., 435 (2011), 578-600.
doi: 10.1016/j.laa.2010.04.048.
|
|
[7]
|
P. Benner, V. Sima and M. Voigt, $\mathcal{L}_∞$-norm computation for continuous-time descriptor systems using structured matrix pencils, IEEE Trans. Automat. Control, 57 (2012), 233-238.
doi: 10.1109/TAC.2011.2161833.
|
|
[8]
|
P. Benner, V. Sima and M. Voigt, Robust and efficient algorithms for $\mathcal{L}_∞$-norm computation for descriptor systems, in Proc. 7th IFAC Symposium on Robust Control Design, IFAC, Aalborg, Denmark, 2012,195-200.
doi: 10.3182/20120620-3-DK-2025.00114.
|
|
[9]
|
P. Benner, V. Sima and M. Voigt, Algorithm 961 -Fortran 77 subroutines for the solution of skew-Hamiltonian/Hamiltonian eigenproblems, ACM Trans. Math. Software, 42, Paper 24.
doi: 10.1145/2818313.
|
|
[10]
|
P. Benner and M. Voigt, A structured pseudospectral method for $\mathcal{H}_∞$-norm computation of large-scale descriptor systems, Math. Control Signals Systems, 26 (2014), 303-338.
doi: 10.1007/s00498-013-0121-7.
|
|
[11]
|
S. Boyd and V. Balakrishnan, A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its $L_∞$-norm, Systems Control Lett., 15 (1990), 1-7.
doi: 10.1016/0167-6911(90)90037-U.
|
|
[12]
|
S. Boyd, V. Balakrishnan and P. Kabamba, A bisection method for computing the $H_{∞}$ norm of a transfer matrix and related problems, Math. Control Signals Systems, 2 (1989), 207-219.
doi: 10.1007/BF02551385.
|
|
[13]
|
N. A. Bruinsma and M. Steinbuch, A fast algorithm to compute the $\mathcal{H}_∞$-norm of a transfer function matrix, Systems Control Lett., 14 (1990), 287-293.
doi: 10.1016/0167-6911(90)90049-Z.
|
|
[14]
|
J. V. Burke, D. Henrion, A. S. Lewis and M. L. Overton, HIFOO-A MATLAB package for fixed-order controller design and $H_∞$ optimization, in Proc. 5th IFAC Syposium on Robust Control Design, Toulouse, France, 2006.
doi: 10.3182/20060705-3-FR-2907.00059.
|
|
[15]
|
Y. Chahlaoui and P. Van Dooren, A collection of benchmark examples for model reduction of linear time invariant dynamical systems, Technical Report 2002-2,2002, Available from http://www.slicot.org/index.php?site=benchmodred.
|
|
[16]
|
M. A. Freitag, A. Spence and P. V. Dooren, Calculating the $H_∞$-norm using the implicit determinant method, SIAM J. Matrix Anal. Appl., 35 (2014), 619-634.
doi: 10.1137/130933228.
|
|
[17]
|
F. Freitas, J. Rommes and N. Martins, Gramian-based reduction method applied to large sparse power system descriptor models, IEEE Trans. Power Syst., 23 (2008), 1258-1270.
doi: 10.1109/TPWRS.2008.926693.
|
|
[18]
|
N. Guglielmi, M. Gürbüzbalaban and M. L. Overton, Fast approximation of the $H_∞$ norm via optimization over spectral value sets, SIAM J. Matrix Anal. Appl., 34 (2013), 709-737.
doi: 10.1137/120875752.
|
|
[19]
|
P. Losse, V. Mehrmann, L. Poppe and T. Reis, The modified optimal $\mathcal H_∞$ control problem for descriptor systems, SIAM J. Control Optim., 47 (2008), 2795-2811.
doi: 10.1137/070710093.
|
|
[20]
|
N. Martins, P. C. Pellanda and J. Rommes, Computation of transfer function dominant zeros with applications to oscillation damping control of large power systems, IEEE Trans. Power Syst., 22 (2007), 1657-1664.
doi: 10.1109/TPWRS.2007.907526.
|
|
[21]
|
V. Mehrmann, C. Schröder and V. Simoncini, An implicitly-restarted Krylov subspace method for real symmetric/skew-symmetric eigenproblems, Linear Algebra Appl., 436 (2012), 4070-4087.
doi: 10.1016/j.laa.2009.11.009.
|
|
[22]
|
V. Mehrmann and T. Stykel, Balanced truncation model reduction for large-scale systems in descriptor form, in Dimension Reduction of Large-Scale Systems (eds. P. Benner, V. Mehrmann and D. Sorensen), vol. 45 of Lecture Notes Comput. Sci. Eng., Springer-Verlag, Berlin, Heidelberg, New York, 2005, chapter 3, 89-116.
doi: 10.1007/3-540-27909-1_3.
|
|
[23]
|
T. Mitchell and M. L. Overton, Fixed low-order controller design and $ H_∞$ optimization for large-scale dynamical systems, in Proc. 8th IFAC Symposium on Robust Control Design, Bratislava, Slovakia, 2015, 25-30.
doi: 10.1016/j.ifacol.2015.09.428.
|
|
[24]
|
T. Mitchell and M. L. Overton, Hybrid expansion-contraction: a robust scaleable method for approxiating the $H_∞$ norm, IMA J. Numer. Anal., 36 (2016), 985-1014.
doi: 10.1093/imanum/drv046.
|
|
[25]
|
J. Rommes, Arnoldi and Jacobi-Davidson methods for generalized eigenvalue problems $Ax = λ Bx$ with singular $B$, Math. Comp., 77 (2008), 995-1015.
doi: 10.1090/S0025-5718-07-02040-6.
|
|
[26]
|
J. Rommes and N. Martins, Efficient computation of multivariable transfer function dominant poles using subspace acceleration, IEEE Trans. Power Syst., 21 (2006), 1471-1487.
doi: 10.1109/TPWRS.2006.881154.
|
|
[27]
|
J. Rommes and G. L. G. Sleijpen, Convergence of the dominant pole algorithm and Rayleigh quotient iteration, SIAM J. Matrix Anal. Appl., 30 (2008), 346-363.
doi: 10.1137/060671401.
|
|
[28]
|
A. Ruhe, Rational Krylov algorithms for nonsymmetric eigenvalue problems, in Recent Advances in Iterative Methods (eds. G. Golub, A. Greenbaum and M. Luskin), vol. 60 of IMA Vol. Math. Appl., Springer-Verlag, New York, 1994,149-164.
doi: 10.1007/978-1-4613-9353-5_10.
|
|
[29]
|
C. Schröder, Private communication, 2013.
|
|
[30]
|
M. Voigt,
On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systems, Logos-Verlag, Berlin, 2015, Also as Dissertation, Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, 2015.
|
|
[31]
|
K. Zhou and J. C. Doyle,
Essentials of Robust Control, Hemel Hempstead: Prentice Hall, 1997.
|
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