Eigenstructure Perturbations for a Class of Hamiltonian Matrices and Solutions of Related Riccati Inequalities

Authors

Volker Mehrmann, Hongguo Xu

Abstract

No available

Citation

• Journal: SIAM Journal on Matrix Analysis and Applications
• Year: 2024
• Volume: 45
• Issue: 3
• Pages: 1335–1360
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/23m1619563

BibTeX

@article{Mehrmann_2024,
  title={{Eigenstructure Perturbations for a Class of Hamiltonian Matrices and Solutions of Related Riccati Inequalities}},
  volume={45},
  ISSN={1095-7162},
  DOI={10.1137/23m1619563},
  number={3},
  journal={SIAM Journal on Matrix Analysis and Applications},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Mehrmann, Volker and Xu, Hongguo},
  year={2024},
  pages={1335--1360}
}

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References

• Bankmann, D., Mehrmann, V., Nesterov, Y. & Van Dooren, P. Computation of the Analytic Center of the Solution Set of the Linear Matrix Inequality Arising in Continuous- and Discrete-Time Passivity Analysis. Vietnam Journal of Mathematics vol. 48 633–659 (2020) – 10.1007/s10013-020-00427-x
• Beattie, C. A., Mehrmann, V. & Van Dooren, P. Robust port-Hamiltonian representations of passive systems. Automatica vol. 100 182–186 (2019) – 10.1016/j.automatica.2018.11.013
• Boyd, S., El Ghaoui, L., Feron, E. & Balakrishnan, V. Linear Matrix Inequalities in System and Control Theory. (1994) doi:10.1137/1.9781611970777 – 10.1137/1.9781611970777
• Cherifi K., Math. Control Signals Systems (2023)
• Faβbender, H., Mackey, D. S., Mackey, N. & Xu, H. Hamiltonian square roots of skew-Hamiltonian matrices. Linear Algebra and its Applications vol. 287 125–159 (1999) – 10.1016/s0024-3795(98)10137-4
• Freiling, G., Mehrmann, V. & Xu, H. Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces. SIAM Journal on Matrix Analysis and Applications vol. 23 1045–1069 (2002) – 10.1137/s0895479800377228
• Gillis, N., Mehrmann, V. & Sharma, P. Computing the nearest stable matrix pairs. Numerical Linear Algebra with Applications vol. 25 (2018) – 10.1002/nla.2153
• Lancaster, P. & Rodman, L. Algebraic Riccati Equations. (1995) doi:10.1093/oso/9780198537953.001.0001 – 10.1093/oso/9780198537953.001.0001
• Lidskii, V. B. Perturbation theory of non-conjugate operators. USSR Computational Mathematics and Mathematical Physics vol. 6 73–85 (1966) – 10.1016/0041-5553(66)90033-4
• Lin, W.-W., Mehrmann, V. & Xu, H. Canonical Forms for Hamiltonian and Symplectic Matrices and Pencils. Linear Algebra and its Applications vols 302–303 469–533 (1999) – 10.1016/s0024-3795(99)00191-3
• The Autonomous Linear Quadratic Control Problem. Lecture Notes in Control and Information Sciences (Springer-Verlag, 1991). doi:10.1007/bfb0039443 – 10.1007/bfb0039443
• Mehrmann, V. & Van Dooren, P. M. Optimal Robustness of Port-Hamiltonian Systems. SIAM Journal on Matrix Analysis and Applications vol. 41 134–151 (2020) – 10.1137/19m1259092
• Mehrmann, V. & Unger, B. Control of port-Hamiltonian differential-algebraic systems and applications. Acta Numerica vol. 32 395–515 (2023) – 10.1017/s0962492922000083
• Mehrmann, V. & Xu, H. Perturbation of purely imaginary eigenvalues of Hamiltonian matrices under structured perturbations. The Electronic Journal of Linear Algebra vol. 17 (2008) – 10.13001/1081-3810.1261
• Moro, J., Burke, J. V. & Overton, M. L. On the Lidskii–Vishik–Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure. SIAM Journal on Matrix Analysis and Applications vol. 18 793–817 (1997) – 10.1137/s0895479895294666
• Van Dooren, P. The computation of Kronecker’s canonical form of a singular pencil. Linear Algebra and its Applications vol. 27 103–140 (1979) – 10.1016/0024-3795(79)90035-1
• Willems, J. Least squares stationary optimal control and the algebraic Riccati equation. IEEE Transactions on Automatic Control vol. 16 621–634 (1971) – 10.1109/tac.1971.1099831
• Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493
• Willems, J. C. Dissipative dynamical systems Part II: Linear systems with quadratic supply rates. Archive for Rational Mechanics and Analysis vol. 45 352–393 (1972) – 10.1007/bf00276494