Stabilization of Linear Port-Hamiltonian Descriptor Systems via Output Feedback

Authors

Delin Chu, Volker Mehrmann

Abstract

Citation

• Journal: SIAM Journal on Matrix Analysis and Applications
• Year: 2025
• Volume: 46
• Issue: 2
• Pages: 1280–1300
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/24m1650259

BibTeX

@article{Chu_2025,
  title={{Stabilization of Linear Port-Hamiltonian Descriptor Systems via Output Feedback}},
  volume={46},
  ISSN={1095-7162},
  DOI={10.1137/24m1650259},
  number={2},
  journal={SIAM Journal on Matrix Analysis and Applications},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Chu, Delin and Mehrmann, Volker},
  year={2025},
  pages={1280--1300}
}

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References

• Achleitner, F., Arnold, A. & Mehrmann, V. Hypocoercivity and controllability in linear semi‐dissipative Hamiltonian ordinary differential equations and differential‐algebraic equations. Z Angew Math Mech 103, (2021) – 10.1002/zamm.202100171
• Aliyev, N., Mehrmann, V. & Mengi, E. Approximation of stability radii for large-scale dissipative Hamiltonian systems. Adv Comput Math 46, (2020) – 10.1007/s10444-020-09763-5
• 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 J. Math. 48, 633–659 (2020) – 10.1007/s10013-020-00427-x
• Beattie, C., Gugercin, S. & Mehrmann, V. Structure-Preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems. Realization and Model Reduction of Dynamical Systems 235–254 (2022) doi:10.1007/978-3-030-95157-3_13 – 10.1007/978-3-030-95157-3_13
• Beattie, C., Mehrmann, V., Xu, H. & Zwart, H. Linear port-Hamiltonian descriptor systems. Math. Control Signals Syst. 30, (2018) – 10.1007/s00498-018-0223-3
• Benner, P., Byers, R., Mehrmann, V. & Xu, H. Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils. SIAM J. Matrix Anal. & Appl. 24, 165–190 (2002) – 10.1137/s0895479800367439
• Brivadis, L., Gauthier, J.-P., Sacchelli, L. & Serres, U. New perspectives on output feedback stabilization at an unobservable target. ESAIM: COCV 27, 102 (2021) – 10.1051/cocv/2021097
• Bunse-Gerstner, A., Byers, R., Mehrmann, V. & Nichols, N. K. Feedback design for regularizing descriptor systems. Linear Algebra and its Applications 299, 119–151 (1999) – 10.1016/s0024-3795(99)00167-6
• Campbell, S. L., Kunkel, P. & Mehrmann, V. Chapter 2: Regularization of Linear and Nonlinear Descriptor Systems. Control and Optimization with Differential-Algebraic Constraints 17–36 (2012) doi:10.1137/9781611972252.ch2 – 10.1137/9781611972252.ch2
• Chu, D. L., Chan, H. C. & Ho, D. W. C. Regularization of Singular Systems by Derivative and Proportional Output Feedback. SIAM J. Matrix Anal. & Appl. 19, 21–38 (1998) – 10.1137/s0895479895270963
• Chu, D. L. & Ho, D. W. C. Necessary and sufficient conditions for the output feedback regularization of descriptor systems. IEEE Trans. Automat. Contr. 44, 405–412 (1999) – 10.1109/9.746277
• Chu, D., Mehrmann, V. & Nichols, N. K. Minimum norm regularization of descriptor systems by mixed output feedback. Linear Algebra and its Applications 296, 39–77 (1999) – 10.1016/s0024-3795(99)00108-1
• Du, N. H., Linh, V. H. & Mehrmann, V. Robust Stability of Differential-Algebraic Equations. Surveys in Differential-Algebraic Equations I 63–95 (2013) doi:10.1007/978-3-642-34928-7_2 – 10.1007/978-3-642-34928-7_2
• Fritzon P., Principles of Object-Oriented Modeling and Simulation with Modelica 2.1 (2003)
• Gantmacher F. R., The Theory of Matrices (1959)
• Gillis, N., Mehrmann, V. & Sharma, P. Computing the nearest stable matrix pairs. Numerical Linear Algebra App 25, (2018) – 10.1002/nla.2153
• Gillis, N. & Sharma, P. On computing the distance to stability for matrices using linear dissipative Hamiltonian systems. Automatica 85, 113–121 (2017) – 10.1016/j.automatica.2017.07.047
• Golub G. H., Matrix Computations (1996)
• Jacob, B. & Zwart, H. J. Linear Port-Hamiltonian Systems on Infinite-Dimensional Spaces. (Springer Basel, 2012). doi:10.1007/978-3-0348-0399-1 – 10.1007/978-3-0348-0399-1
• Kailath T., Linear Systems (1980)
• Kunkel, P. & Mehrmann, V. Differential-Algebraic Equations. EMS Textbooks in Mathematics (2006) doi:10.4171/017 – 10.4171/017
• Linh, V. H. & Mehrmann, V. Lyapunov, Bohl and Sacker-Sell Spectral Intervals for Differential-Algebraic Equations. J Dyn Diff Equat 21, 153–194 (2009) – 10.1007/s10884-009-9128-7
• Mehl, C., Mehrmann, V. & Wojtylak, M. Linear Algebra Properties of Dissipative Hamiltonian Descriptor Systems. SIAM J. Matrix Anal. & Appl. 39, 1489–1519 (2018) – 10.1137/18m1164275
• Mehl, C., Mehrmann, V. & Wojtylak, M. Distance problems for dissipative Hamiltonian systems and related matrix polynomials. Linear Algebra and its Applications 623, 335–366 (2021) – 10.1016/j.laa.2020.05.026
• Mehrmann, V. & Van Dooren, P. M. Optimal Robustness of Port-Hamiltonian Systems. SIAM J. Matrix Anal. Appl. 41, 134–151 (2020) – 10.1137/19m1259092
• Mehrmann, V. & Unger, B. Control of port-Hamiltonian differential-algebraic systems and applications. Acta Numerica 32, 395–515 (2023) – 10.1017/s0962492922000083
• Mehrmann, V. & van der Schaft, A. Differential–algebraic systems with dissipative Hamiltonian structure. Math. Control Signals Syst. 35, 541–584 (2023) – 10.1007/s00498-023-00349-2
• Nichols, N. K. & Chu, D. Regularization of Descriptor Systems. Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory 415–433 (2015) doi:10.1007/978-3-319-15260-8_15 – 10.1007/978-3-319-15260-8_15
• Ozcaldiran, K. & Lewis, F. L. On the regularizability of singular systems. IEEE Trans. Automat. Contr. 35, 1156–1160 (1990) – 10.1109/9.58561
• Shayman, M. & Zheng Zhou. Feedback control and classification of generalized linear systems. IEEE Trans. Automat. Contr. 32, 483–494 (1987) – 10.1109/tac.1987.1104642
• Syrmos, V. L., Abdallah, C. T., Dorato, P. & Grigoriadis, K. Static output feedback—A survey. Automatica 33, 125–137 (1997) – 10.1016/s0005-1098(96)00141-0
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. FnT in Systems and Control 1, 173–378 (2014) – 10.1561/2600000002
• van der Schaft, A. & Mehrmann, V. Linear port-Hamiltonian DAE systems revisited. Systems & Control Letters 177, 105564 (2023) – 10.1016/j.sysconle.2023.105564
• Zhou K., Robust and Optimal Control (1995)