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Mathematical and Computer Modelling of Dynamical Systems
Methods, Tools and Applications in Engineering and Related Sciences
Volume 17, 2011 - Issue 2
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Articles

Efficient balancing-based MOR for large-scale second-order systems

Peter Benner Department of Mathematics in Industry and Technology, Faculty of Mathematics, TU Chemnitz, Germany; Department of Computational Methods in Systems and Control Theory, Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
&
Jens Saak Department of Computational Methods in Systems and Control Theory, Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg, GermanyCorrespondence[email protected]
Pages 123-143 | Received 03 Mar 2010, Accepted 08 Nov 2010, Published online: 23 Feb 2011

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Peter Benner, Jens Saak & M. Monir Uddin. (2016) Structure preserving model order reduction of large sparse second-order index-1 systems and application to a mechatronics model. Mathematical and Computer Modelling of Dynamical Systems 22:6, pages 509-523.
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Zhi-Hua Xiao & Yao-Lin Jiang. (2014) Dimension reduction for second-order systems by general orthogonal polynomials. Mathematical and Computer Modelling of Dynamical Systems 20:4, pages 414-432.
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Peter Benner, Patrick Kürschner & Jens Saak. (2013) An improved numerical method for balanced truncation for symmetric second-order systems. Mathematical and Computer Modelling of Dynamical Systems 19:6, pages 593-615.
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Articles from other publishers (36)

Mahtab Uddin, Md. Toriqul Islam, M. Monir Uddin & M. A. Hakim Khan. (2022) Riccati-based feedback stabilization of incompressible Navier-Stokes models via reduced-order modelling by iterative rational Krylov algorithm. Riccati-based feedback stabilization of incompressible Navier-Stokes models via reduced-order modelling by iterative rational Krylov algorithm.
Liu Dai, Zhi-Hua Xiao, Ren-Zheng Zhang & Yao-Lin Jiang. (2021) Laguerre-Gramian-based structure-preserving model order reduction for second-order form systems. Transactions of the Institute of Measurement and Control 44:5, pages 1113-1124.
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Rahila Malik, Mehboob Alam, Shah Muhammad, Faisal Zaid Duraihem & Yehia Massoud. (2022) Second-Order Arnoldi Reduction Using Weighted Gaussian Kernel. IEEE Access 10, pages 41362-41370.
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Peter Benner, Serkan Gugercin & Steffen W. R. Werner. (2021) Structure-preserving interpolation of bilinear control systems. Advances in Computational Mathematics 47:3.
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Mahtab Uddin, M Monir Uddin, M A Hakim Khan & Md Motlubar Rahman. (2021) Interpolatory projection technique for Riccati-based feedback stabilization of index-1 descriptor systems. IOP Conference Series: Materials Science and Engineering 1070:1, pages 012022.
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Ines Dorschky, Timo Reis & Matthias Voigt. (2021) Balanced Truncation Model Reduction for Symmetric Second Order Systems---A Passivity-Based Approach. SIAM Journal on Matrix Analysis and Applications 42:4, pages 1602-1635.
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Md. Motlubar Rahman, Mohammad Monir Uddin, Laek Sazzad Andallah & Mahtab Uddin. (2020) Interpolatory Projection Techniques for H2 Optimal Structure-Preserving Model Order Reduction of Second-Order Systems. Advances in Science, Technology and Engineering Systems Journal 5:4, pages 715-723.
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M. Monir Uddin. 2020. Proceedings of International Joint Conference on Computational Intelligence. Proceedings of International Joint Conference on Computational Intelligence 487 496 .
Rebekka S. Beddig, Peter Benner, Ines Dorschky, Timo Reis, Paul Schwerdtner, Matthias Voigt & Steffen W. R. Werner. (2019) Model Reduction for Second‐Order Dynamical Systems Revisited. PAMM 19:1.
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Jens Saak, Dirk Siebelts & Steffen W. R. Werner. (2019) A comparison of second-order model order reduction methods for an artificial fishtail. at - Automatisierungstechnik 67:8, pages 648-667.
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Zhi‐Hua Xiao, Yao‐Lin Jiang & Zhen‐Zhong Qi. (2019) Structure preserving balanced proper orthogonal decomposition for second‐order form systems via shifted Legendre polynomials. IET Control Theory & Applications 13:8, pages 1155-1165.
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M. Monir Uddin. (2018) Gramian‐based model‐order reduction of constrained structural dynamic systems. IET Control Theory & Applications 12:17, pages 2337-2346.
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Xiaomei Lu, Wu‐Hua Chen & Feifei Xue. (2018) Impulsive natural observers for vector second‐order Lipschitz non‐linear systems. IET Control Theory & Applications 12:9, pages 1349-1356.
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Zhi-Yong Qiu, Yao-Lin Jiang & Jia-Wei Yuan. (2018) Interpolatory Model Order Reduction Method for Second Order Systems. Asian Journal of Control 20:1, pages 312-322.
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Daniela Oetinger, Eckhard Arnold & Oliver Sawodny. (2017) Model based controller design for the compensation of thermally induced deformations. Production Engineering 11:4-5, pages 601-611.
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M. Monir Uddin. (2017) Structure preserving model order reduction using the projection onto the dominant eigen-space of the Gramian (PDEG). Structure preserving model order reduction using the projection onto the dominant eigen-space of the Gramian (PDEG).
Peter Benner & Tatjana Stykel. 2017. Surveys in Differential-Algebraic Equations IV. Surveys in Differential-Algebraic Equations IV 107 160 .
Tatjana Stykel & Alexander Vasilyev. (2016) A two-step model reduction approach for mechanical systems with moving loads. Journal of Computational and Applied Mathematics 297, pages 85-97.
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Daniela Oetinger & Oliver Sawodny. (2015) Using model order reduction for disturbance feed forward control based on transient thermal finite element models. Using model order reduction for disturbance feed forward control based on transient thermal finite element models.
Salim Ibrir. (2015) Improving the transient response in backstepping control designs: Application to robotic manipulators. Improving the transient response in backstepping control designs: Application to robotic manipulators.
Jia-Wei Yuan, Yao-Lin Jiang & Zhi-Hua Xiao. (2015) Structure-preserving model order reduction by general orthogonal polynomials for integral–differential systems. Journal of the Franklin Institute 352:1, pages 138-154.
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Philip Holzwarth & Peter Eberhard. (2015) SVD-based improvements for component mode synthesis in elastic multibody systems. European Journal of Mechanics - A/Solids 49, pages 408-418.
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Michael Fischer & Peter Eberhard. (2013) Linear model reduction of large scale industrial models in elastic multibody dynamics. Multibody System Dynamics 31:1, pages 27-46.
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J. Fehr, M. Fischer, B. Haasdonk & P. Eberhard. (2012) Greedy‐based approximation of frequency‐weighted Gramian matrices for model reduction in multibody dynamics. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 93:8, pages 501-519.
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Elias Jarlebring, Tobias Damm & Wim Michiels. (2012) Model reduction of time-delay systems using position balancing and delay Lyapunov equations. Mathematics of Control, Signals, and Systems 25:2, pages 147-166.
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C. Nowakowski, P. Kürschner, P. Eberhard & P. Benner. (2012) Model reduction of an elastic crankshaft for elastic multibody simulations. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 93:4, pages 198-216.
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Jan Lienemann, Emanuele Bertarelli, Andreas Greiner & Jan G. Korvink. 2013. System‐Level Modeling of MEMS. System‐Level Modeling of MEMS 263 289 .
Peter Benner, Patrick Kürschner & Jens Saak. (2012) Efficient handling of complex shift parameters in the low-rank Cholesky factor ADI method. Numerical Algorithms 62:2, pages 225-251.
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Peter Benner, Zoran Tomljanović & Ninoslav Truhar. (2013) Optimal damping of selected eigenfrequencies using dimension reduction. Numerical Linear Algebra with Applications 20:1, pages 1-17.
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Peter Benner, Jens Saak & M. Monir Uddin. (2012) Second order to second order balancing for index-1 vibrational systems. Second order to second order balancing for index-1 vibrational systems.
Mohammad Monir Uddin, Jens Saak, Burkhard Kranz & Peter Benner. (2012) Computation of a compact state space model for an adaptive spindle head configuration with piezo actuators using balanced truncation. Production Engineering 6:6, pages 577-586.
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Peter Benner, Burkhard Kranz, Jens Saak & M. Monir Uddin. (2012) Efficient Reduced Order State Space Model Computation for a Class of Second Order Index One Systems. PAMM 12:1, pages 699-700.
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Peter Benner, Patrick Kürschner & Jens Saak. (2012) Avoiding complex arithmetic in the low-rank ADI method efficiently. PAMM 12:1, pages 639-640.
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Wolfgang Witteveen. (2012) On the Modal and Non-Modal Model Reduction of Metallic Structures with Variable Boundary Conditions. World Journal of Mechanics 02:06, pages 311-324.
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Peter Benner, Patrick Kürschner & Jens Saak. (2012) Improved Second-Order Balanced Truncation for Symmetric Systems. IFAC Proceedings Volumes 45:2, pages 758-762.
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Wolfgang Witteveen. 2012. Topics in Experimental Dynamics Substructuring and Wind Turbine Dynamics, Volume 2. Topics in Experimental Dynamics Substructuring and Wind Turbine Dynamics, Volume 2 319 331 .

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