 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. Google Scholar 
[2] 
P. Benner, Solving largescale control problems, IEEE Control System Magazine, 24 (2004), 4459. Google Scholar 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275296. doi: 10.1002/gamm.201490034. Google Scholar 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, SpringerVerlag, London, 2009. Google Scholar 
[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. Google Scholar 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. Google Scholar 
[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. Google Scholar 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267319. doi: 10.1017/S0962492902000120. Google Scholar 
[9] 
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. Google Scholar 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[17] 
J. Phillips, Model reduction of timevarying linear systems using multipoint Krylovsubspace projectors, in International Conference on ComputerAided Design, ACM, 1998, 96102. Google Scholar 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems, IEEE Trans. ComputerAided Design, 22 (2003), 171187. Google Scholar 
[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. Google Scholar 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems, IEEE Control Systems Magazine, 46 (1999), 12731288. Google Scholar 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems, in ASPDAC '99. Asia and South Pacific, IEEE, 1999, 5356. Google Scholar 
[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. Google Scholar 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003. doi: 10.1137/1.9780898718003. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[26] 
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , (). Google Scholar 
[27] 
T. Stykel, Lowrank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187202. Google Scholar 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480484. Google Scholar 
[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. Google Scholar 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 5693. Google Scholar 
[31] 
E. Wachspress, The ADI Model Problem,, 1995, (). Google Scholar 
[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. Google Scholar 
[33] 
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291299. Google Scholar 
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. Google Scholar 
[2] 
P. Benner, Solving largescale control problems, IEEE Control System Magazine, 24 (2004), 4459. Google Scholar 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation, GAMM Mitteilungen, 23 (2006), 275296. doi: 10.1002/gamm.201490034. Google Scholar 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control, 1st edition, SpringerVerlag, London, 2009. Google Scholar 
[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. Google Scholar 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis, Ninth edition, Brooks/Cole, Boston, USA, 2011. Google Scholar 
[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. Google Scholar 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces, Acta Numerica, 12 (2003), 267319. doi: 10.1017/S0962492902000120. Google Scholar 
[9] 
G. Golub and C. Van Loan, Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, 1996. Google Scholar 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction, Ph.D. thesis, University of Illinois at Urbana, Champaign, 1997. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[17] 
J. Phillips, Model reduction of timevarying linear systems using multipoint Krylovsubspace projectors, in International Conference on ComputerAided Design, ACM, 1998, 96102. Google Scholar 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems, IEEE Trans. ComputerAided Design, 22 (2003), 171187. Google Scholar 
[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. Google Scholar 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems, IEEE Control Systems Magazine, 46 (1999), 12731288. Google Scholar 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems, in ASPDAC '99. Asia and South Pacific, IEEE, 1999, 5356. Google Scholar 
[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. Google Scholar 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003. doi: 10.1137/1.9780898718003. Google Scholar 
[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. Google Scholar 
[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. Google Scholar 
[26] 
R. E. Skelton, M. Oliveira and J. Han, System modeling and model reduction,, Paper available from: , (). Google Scholar 
[27] 
T. Stykel, Lowrank iterative methods for projected generalized Lyapunov equations, Electron. Trans. Numer. Anal., 30 (2008), 187202. Google Scholar 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods, in 32rd Design Automation Conference, IEEE, 1995, 480484. Google Scholar 
[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. Google Scholar 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial, in IEEE Proceedings, IEEE, 1990, 5693. Google Scholar 
[31] 
E. Wachspress, The ADI Model Problem,, 1995, (). Google Scholar 
[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. Google Scholar 
[33] 
L. Zadeh, Frequency analysis of variable networks, IEEE Transactions on Circuits and Systems, 38 (1950), 291299. Google Scholar 
[1] 
Elimhan N. Mahmudov. Second order discrete timevarying and timeinvariant linear continuous systems and Kalman type conditions. Numerical Algebra, Control & Optimization, 2021 doi: 10.3934/naco.2021010 
[2] 
Le Viet Cuong, Thai Son Doan. Assignability of dichotomy spectra for discrete timevarying linear control systems. Discrete & Continuous Dynamical Systems  B, 2020, 25 (9) : 35973607. doi: 10.3934/dcdsb.2020074 
[3] 
Abdelfettah Hamzaoui, Nizar Hadj Taieb, Mohamed Ali Hammami. Practical partial stability of timevarying systems. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021197 
[4] 
K. Aruna Sakthi, A. Vinodkumar. Stabilization on input timevarying delay for linear switched systems with truncated predictor control. Numerical Algebra, Control & Optimization, 2020, 10 (2) : 237247. doi: 10.3934/naco.2019050 
[5] 
Hongjie Dong, Seick Kim. Green's functions for parabolic systems of second order in timevarying domains. Communications on Pure & Applied Analysis, 2014, 13 (4) : 14071433. doi: 10.3934/cpaa.2014.13.1407 
[6] 
Roberta Fabbri, Russell Johnson, Sylvia Novo, Carmen Núñez. On linearquadratic dissipative control processes with timevarying coefficients. Discrete & Continuous Dynamical Systems, 2013, 33 (1) : 193210. doi: 10.3934/dcds.2013.33.193 
[7] 
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 & Optimization, 2021 doi: 10.3934/naco.2021016 
[8] 
Abdeslem Hafid Bentbib, Smahane ElHalouy, El Mostafa Sadek. Extended Krylov subspace methods for solving Sylvester and Stein tensor equations. Discrete & Continuous Dynamical Systems  S, 2021 doi: 10.3934/dcdss.2021026 
[9] 
Qiao Liang, Qiang Ye. Deflation by restriction for the inversefree preconditioned Krylov subspace method. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 5571. doi: 10.3934/naco.2016.6.55 
[10] 
Tingwen Huang, Guanrong Chen, Juergen Kurths. Synchronization of chaotic systems with timevarying coupling delays. Discrete & Continuous Dynamical Systems  B, 2011, 16 (4) : 10711082. doi: 10.3934/dcdsb.2011.16.1071 
[11] 
Shu Zhang, Jian Xu. Timevarying delayed feedback control for an internet congestion control model. Discrete & Continuous Dynamical Systems  B, 2011, 16 (2) : 653668. doi: 10.3934/dcdsb.2011.16.653 
[12] 
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 
[13] 
Charles L. Epstein, Leslie Greengard, Thomas Hagstrom. On the stability of timedomain integral equations for acoustic wave propagation. Discrete & Continuous Dynamical Systems, 2016, 36 (8) : 43674382. doi: 10.3934/dcds.2016.36.4367 
[14] 
Gang Bao, Bin Hu, Peijun Li, Jue Wang. Analysis of timedomain Maxwell's equations in biperiodic structures. Discrete & Continuous Dynamical Systems  B, 2020, 25 (1) : 259286. doi: 10.3934/dcdsb.2019181 
[15] 
Lu Zhao, Heping Dong, Fuming Ma. Timedomain analysis of forward obstacle scattering for elastic wave. Discrete & Continuous Dynamical Systems  B, 2021, 26 (8) : 41114130. doi: 10.3934/dcdsb.2020276 
[16] 
Lijuan Wang, Yashan Xu. Admissible controls and controllable sets for a linear timevarying ordinary differential equation. Mathematical Control & Related Fields, 2018, 8 (3&4) : 10011019. doi: 10.3934/mcrf.2018043 
[17] 
Carlos Nonato, Manoel Jeremias dos Santos, Carlos Raposo. Dynamics of Timoshenko system with timevarying weight and timevarying delay. Discrete & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021053 
[18] 
Dinh Cong Huong, Mai Viet Thuan. State transformations of timevarying delay systems and their applications to state observer design. Discrete & Continuous Dynamical Systems  S, 2017, 10 (3) : 413444. doi: 10.3934/dcdss.2017020 
[19] 
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 
[20] 
Larbi Berrahmoune. Null controllability for distributed systems with timevarying constraint and applications to paraboliclike equations. Discrete & Continuous Dynamical Systems  B, 2020, 25 (8) : 32753303. doi: 10.3934/dcdsb.2020062 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]