 Previous Article
 NACO Home
 This Issue

Next Article
Deflation by restriction for the inversefree preconditioned Krylov subspace method
Projectionbased model reduction for timevarying descriptor systems: New results
1.  Department of Mathematics and Physics, North South University, Dhaka, Bangladesh 
References:
[1] 
Z. Bai, Krylov subspace techniques for reducedorder modeling for largescale dynamical system, App. Numer. Math, 43(12) (2002), 944. doi: 10.1016/S01689274(02)001162. 
[2] 
P. Benner, Solving largescale control problems, IEEE Control System Magazine, 24 (2004), 4459. 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275296. doi: 10.1002/gamm.201490034. 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, SpringerVerlag, London, 2009. 
[5] 
H. G. Brachtendorf, Theorie und Analyse von Autonomen und Quasiperiodisch Angeregten Elektrischen Netzwerken. Eine Algorithmisch Orientierte Betrachtung, Habilitation thesis, University of Bremen, Germany, 2001. 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. 
[7] 
I. Elfadel and D. D. Ling, A block Arnoldi algorithm for multipoint passive modelorder reduction of multiport RLC networks, in IEEE/ACM International Conference on ComputerAided Design, IEEE, (1997), 6671. 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267319. doi: 10.1017/S0962492902000120. 
[9] 
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. 
[11] 
S. Gugercin, An iterative SVDKRYLOV based method for model reduction of largescale dynamical systems, in 44'th IEEE Conference on Decision and Control and the European control conference, IEEE, 2005, 59055910. 
[12] 
S. Gugercin, A. C. Antoulas and C. Beattie, H_{2} model reduction for largescale linear dynamical systems, SIAM J. Matrix Anal. Appl, 30 (2008), 609638. doi: 10.1137/060666123. 
[13] 
M.S. Hossain and P. Benner, Projectionbased model reduction for timevarying descriptor systems using recycled Krylov subspaces, in Appllied Mathematics and Mechanics, WILEYVCH Verlag, 2008, 1008110084. 
[14] 
M. Nakhla and E. Gad, Efficient model reduction of linear timevarying systems via compressed transient system function, in Conference on Design, automation and test in Europe, IEEE, 2002, 916922. 
[15] 
M. Nakhla and E. Gad, Efficient model reduction of linear periodically timevarying systems via compressed transient system function, IEEE Transactions on Circuit and Systems, 52 (2005), 11881204. doi: 10.1109/TCSI.2005.846661. 
[16] 
T. Penzl, Algorithms for model reduction of large dynamical systems, Linear Algebra Appl., 415 (2006), 322343. doi: 10.1016/j.laa.2006.01.007. 
[17] 
J. Phillips, Model reduction of timevarying linear systems using multipoint Krylovsubspace projectors, in International Conference on ComputerAided Design, ACM, 1998, 96102. 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems, IEEE Trans. ComputerAided Design, 22 (2003), 171187. 
[19] 
A. Rahman and M. S. Hossain, SvdKrylov based model reduction for timevarying periodic descriptor systems, in 2nd International Conference on Electrical Engineering and Information Technology, IEEE, 2015. 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems, IEEE Control Systems Magazine, 46 (1999), 12731288. 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems, in ASPDAC '99. Asia and South Pacific, IEEE, 1999, 5356. 
[22] 
Y. Saad, Overview of Krylov subspace methods with applications to control problems, in International Symposium MTNS89 on Signal Processing, Scattering and Operator Theory, and Numerical Methods, Birkhauser Verlag AG, 1990. 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003. doi: 10.1137/1.9780898718003. 
[24] 
B. Salimbahrami, B. Lohmann, T. Bechtold and J. Korvink, Twosided Arnoldi algorithm and its application in order reduction of MEMS, in 4th Fourth International Conference on Mathematical Modelling (eds. I. Troch and F. Breitenecker), Vienna, 2003, 10211028. 
[25] 
S. B. Salimbahrami, Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technische Universität München, Fakultät für Maschinenwesen, Germany, 2005. 
[26] 
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , (). 
[27] 
T. Stykel, Lowrank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187202. 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480484. 
[29] 
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of twotone RF circuits, in 33rd annual Design Automation Conference, IEEE, 1996, 292297. 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 5693. 
[31]  
[32] 
B. Yang and D. Feng, Efficient finitedifference method for quasiperiodic steadystate and small signal analyses, in IEEE/ACM International Conference on ComputerAided Design, IEEE, 2000, 272276. 
[33] 
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291299. 
show all references
References:
[1] 
Z. Bai, Krylov subspace techniques for reducedorder modeling for largescale dynamical system, App. Numer. Math, 43(12) (2002), 944. doi: 10.1016/S01689274(02)001162. 
[2] 
P. Benner, Solving largescale control problems, IEEE Control System Magazine, 24 (2004), 4459. 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275296. doi: 10.1002/gamm.201490034. 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, SpringerVerlag, London, 2009. 
[5] 
H. G. Brachtendorf, Theorie und Analyse von Autonomen und Quasiperiodisch Angeregten Elektrischen Netzwerken. Eine Algorithmisch Orientierte Betrachtung, Habilitation thesis, University of Bremen, Germany, 2001. 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. 
[7] 
I. Elfadel and D. D. Ling, A block Arnoldi algorithm for multipoint passive modelorder reduction of multiport RLC networks, in IEEE/ACM International Conference on ComputerAided Design, IEEE, (1997), 6671. 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267319. doi: 10.1017/S0962492902000120. 
[9] 
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. 
[11] 
S. Gugercin, An iterative SVDKRYLOV based method for model reduction of largescale dynamical systems, in 44'th IEEE Conference on Decision and Control and the European control conference, IEEE, 2005, 59055910. 
[12] 
S. Gugercin, A. C. Antoulas and C. Beattie, H_{2} model reduction for largescale linear dynamical systems, SIAM J. Matrix Anal. Appl, 30 (2008), 609638. doi: 10.1137/060666123. 
[13] 
M.S. Hossain and P. Benner, Projectionbased model reduction for timevarying descriptor systems using recycled Krylov subspaces, in Appllied Mathematics and Mechanics, WILEYVCH Verlag, 2008, 1008110084. 
[14] 
M. Nakhla and E. Gad, Efficient model reduction of linear timevarying systems via compressed transient system function, in Conference on Design, automation and test in Europe, IEEE, 2002, 916922. 
[15] 
M. Nakhla and E. Gad, Efficient model reduction of linear periodically timevarying systems via compressed transient system function, IEEE Transactions on Circuit and Systems, 52 (2005), 11881204. doi: 10.1109/TCSI.2005.846661. 
[16] 
T. Penzl, Algorithms for model reduction of large dynamical systems, Linear Algebra Appl., 415 (2006), 322343. doi: 10.1016/j.laa.2006.01.007. 
[17] 
J. Phillips, Model reduction of timevarying linear systems using multipoint Krylovsubspace projectors, in International Conference on ComputerAided Design, ACM, 1998, 96102. 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems, IEEE Trans. ComputerAided Design, 22 (2003), 171187. 
[19] 
A. Rahman and M. S. Hossain, SvdKrylov based model reduction for timevarying periodic descriptor systems, in 2nd International Conference on Electrical Engineering and Information Technology, IEEE, 2015. 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems, IEEE Control Systems Magazine, 46 (1999), 12731288. 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems, in ASPDAC '99. Asia and South Pacific, IEEE, 1999, 5356. 
[22] 
Y. Saad, Overview of Krylov subspace methods with applications to control problems, in International Symposium MTNS89 on Signal Processing, Scattering and Operator Theory, and Numerical Methods, Birkhauser Verlag AG, 1990. 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003. doi: 10.1137/1.9780898718003. 
[24] 
B. Salimbahrami, B. Lohmann, T. Bechtold and J. Korvink, Twosided Arnoldi algorithm and its application in order reduction of MEMS, in 4th Fourth International Conference on Mathematical Modelling (eds. I. Troch and F. Breitenecker), Vienna, 2003, 10211028. 
[25] 
S. B. Salimbahrami, Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technische Universität München, Fakultät für Maschinenwesen, Germany, 2005. 
[26] 
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , (). 
[27] 
T. Stykel, Lowrank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187202. 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480484. 
[29] 
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of twotone RF circuits, in 33rd annual Design Automation Conference, IEEE, 1996, 292297. 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 5693. 
[31]  
[32] 
B. Yang and D. Feng, Efficient finitedifference method for quasiperiodic steadystate and small signal analyses, in IEEE/ACM International Conference on ComputerAided Design, IEEE, 2000, 272276. 
[33] 
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291299. 
[1] 
Kun Li, TingZhu Huang, Liang Li, Ying Zhao, Stéphane Lanteri. A nonintrusive model order reduction approach for parameterized timedomain Maxwell's equations. Discrete and Continuous Dynamical Systems  B, 2022 doi: 10.3934/dcdsb.2022084 
[2] 
Elimhan N. Mahmudov. Second order discrete timevarying and timeinvariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 353371. doi: 10.3934/naco.2021010 
[3] 
Le Viet Cuong, Thai Son Doan. Assignability of dichotomy spectra for discrete timevarying linear control systems. Discrete and Continuous Dynamical Systems  B, 2020, 25 (9) : 35973607. doi: 10.3934/dcdsb.2020074 
[4] 
Abdelfettah Hamzaoui, Nizar Hadj Taieb, Mohamed Ali Hammami. Practical partial stability of timevarying systems. Discrete and Continuous Dynamical Systems  B, 2022, 27 (7) : 35853603. doi: 10.3934/dcdsb.2021197 
[5] 
K. Aruna Sakthi, A. Vinodkumar. Stabilization on input timevarying delay for linear switched systems with truncated predictor control. Numerical Algebra, Control and Optimization, 2020, 10 (2) : 237247. doi: 10.3934/naco.2019050 
[6] 
Hongjie Dong, Seick Kim. Green's functions for parabolic systems of second order in timevarying domains. Communications on Pure and Applied Analysis, 2014, 13 (4) : 14071433. doi: 10.3934/cpaa.2014.13.1407 
[7] 
Roberta Fabbri, Russell Johnson, Sylvia Novo, Carmen Núñez. On linearquadratic dissipative control processes with timevarying coefficients. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 193210. doi: 10.3934/dcds.2013.33.193 
[8] 
Xin Du, M. Monir Uddin, A. Mostakim Fony, Md. Tanzim Hossain, Md. Nazmul Islam Shuzan. Iterative Rational Krylov Algorithms for model reduction of a class of constrained structural dynamic system with Engineering applications. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021016 
[9] 
Qiao Liang, Qiang Ye. Deflation by restriction for the inversefree preconditioned Krylov subspace method. Numerical Algebra, Control and Optimization, 2016, 6 (1) : 5571. doi: 10.3934/naco.2016.6.55 
[10] 
Abdeslem Hafid Bentbib, Smahane ElHalouy, El Mostafa Sadek. Extended Krylov subspace methods for solving Sylvester and Stein tensor equations. Discrete and Continuous Dynamical Systems  S, 2022, 15 (1) : 4156. doi: 10.3934/dcdss.2021026 
[11] 
Tingwen Huang, Guanrong Chen, Juergen Kurths. Synchronization of chaotic systems with timevarying coupling delays. Discrete and Continuous Dynamical Systems  B, 2011, 16 (4) : 10711082. doi: 10.3934/dcdsb.2011.16.1071 
[12] 
Shu Zhang, Jian Xu. Timevarying delayed feedback control for an internet congestion control model. Discrete and Continuous Dynamical Systems  B, 2011, 16 (2) : 653668. doi: 10.3934/dcdsb.2011.16.653 
[13] 
Robert G. McLeod, John F. Brewster, Abba B. Gumel, Dean A. Slonowsky. Sensitivity and uncertainty analyses for a SARS model with timevarying inputs and outputs. Mathematical Biosciences & Engineering, 2006, 3 (3) : 527544. doi: 10.3934/mbe.2006.3.527 
[14] 
Charles L. Epstein, Leslie Greengard, Thomas Hagstrom. On the stability of timedomain integral equations for acoustic wave propagation. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 43674382. doi: 10.3934/dcds.2016.36.4367 
[15] 
Gang Bao, Bin Hu, Peijun Li, Jue Wang. Analysis of timedomain Maxwell's equations in biperiodic structures. Discrete and Continuous Dynamical Systems  B, 2020, 25 (1) : 259286. doi: 10.3934/dcdsb.2019181 
[16] 
Lu Zhao, Heping Dong, Fuming Ma. Timedomain analysis of forward obstacle scattering for elastic wave. Discrete and Continuous Dynamical Systems  B, 2021, 26 (8) : 41114130. doi: 10.3934/dcdsb.2020276 
[17] 
Lijuan Wang, Yashan Xu. Admissible controls and controllable sets for a linear timevarying ordinary differential equation. Mathematical Control and Related Fields, 2018, 8 (3&4) : 10011019. doi: 10.3934/mcrf.2018043 
[18] 
Carlos Nonato, Manoel Jeremias dos Santos, Carlos Raposo. Dynamics of Timoshenko system with timevarying weight and timevarying delay. Discrete and Continuous Dynamical Systems  B, 2022, 27 (1) : 523553. doi: 10.3934/dcdsb.2021053 
[19] 
Dinh Cong Huong, Mai Viet Thuan. State transformations of timevarying delay systems and their applications to state observer design. Discrete and Continuous Dynamical Systems  S, 2017, 10 (3) : 413444. doi: 10.3934/dcdss.2017020 
[20] 
Wei Feng, Xin Lu. Global stability in a class of reactiondiffusion systems with timevarying delays. Conference Publications, 1998, 1998 (Special) : 253261. doi: 10.3934/proc.1998.1998.253 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]