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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), 1. doi: 10.1016/S01689274(02)001162. 
[2] 
P. Benner, Solving largescale control problems,, IEEE Control System Magazine, 24 (2004), 44. 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation,, GAMM Mitteilungen, 23 (2006), 275. doi: 10.1002/gamm.201490034. 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control,, 1st edition, (2009). 
[5] 
H. G. Brachtendorf, Theorie und Analyse von Autonomen und Quasiperiodisch Angeregten Elektrischen Netzwerken. Eine Algorithmisch Orientierte Betrachtung,, Habilitation thesis, (2001). 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis,, Ninth edition, (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, (1997), 66. 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces,, Acta Numerica, 12 (2003), 267. doi: 10.1017/S0962492902000120. 
[9] 
G. Golub and C. Van Loan, Matrix Computations,, 3rd edition, (1996). 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction,, Ph.D. thesis, (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, (2005), 5905. 
[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), 609. 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, (2008), 10081. 
[14] 
M. Nakhla and E. Gad, Efficient model reduction of linear timevarying systems via compressed transient system function,, in Conference on Design, (2002), 916. 
[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), 1188. doi: 10.1109/TCSI.2005.846661. 
[16] 
T. Penzl, Algorithms for model reduction of large dynamical systems,, Linear Algebra Appl., 415 (2006), 322. 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, (1998), 96. 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems,, IEEE Trans. ComputerAided Design, 22 (2003), 171. 
[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, (2015). 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems,, IEEE Control Systems Magazine, 46 (1999), 1273. 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems,, in ASPDAC '99. Asia and South Pacific, (1999), 53. 
[22] 
Y. Saad, Overview of Krylov subspace methods with applications to control problems,, in International Symposium MTNS89 on Signal Processing, (1990). 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems,, 2nd edition, (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), (2003), 1021. 
[25] 
S. B. Salimbahrami, Structure Preserving Order Reduction of Large Scale Second Order Models,, Ph.D. thesis, (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), 187. 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods,, in 32rd Design Automation Conference, (1995), 480. 
[29] 
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of twotone RF circuits,, in 33rd annual Design Automation Conference, (1996), 292. 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial,, in IEEE Proceedings, (1990), 56. 
[31] 
E. Wachspress, The ADI Model Problem,, 1995, (). 
[32] 
B. Yang and D. Feng, Efficient finitedifference method for quasiperiodic steadystate and small signal analyses,, in IEEE/ACM International Conference on ComputerAided Design, (2000), 272. 
[33] 
L. Zadeh, Frequency analysis of variable networks,, IEEE Transactions on Circuits and Systems, 38 (1950), 291. 
show all references
References:
[1] 
Z. Bai, Krylov subspace techniques for reducedorder modeling for largescale dynamical system,, App. Numer. Math, 43(12) (2002), 1. doi: 10.1016/S01689274(02)001162. 
[2] 
P. Benner, Solving largescale control problems,, IEEE Control System Magazine, 24 (2004), 44. 
[3] 
P. Benner, Numerical linear algebra for model reduction in control and simulation,, GAMM Mitteilungen, 23 (2006), 275. doi: 10.1002/gamm.201490034. 
[4] 
S. Bittanti and P. Colaneri, Periodic Systems: Filtering and Control,, 1st edition, (2009). 
[5] 
H. G. Brachtendorf, Theorie und Analyse von Autonomen und Quasiperiodisch Angeregten Elektrischen Netzwerken. Eine Algorithmisch Orientierte Betrachtung,, Habilitation thesis, (2001). 
[6] 
R. L. Burden and J. D. Faires, Numerical Analysis,, Ninth edition, (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, (1997), 66. 
[8] 
R. Freund, Model reduction methods based on Krylov subspaces,, Acta Numerica, 12 (2003), 267. doi: 10.1017/S0962492902000120. 
[9] 
G. Golub and C. Van Loan, Matrix Computations,, 3rd edition, (1996). 
[10] 
E. J. Grimme, Kryloy projection methods for model reduction,, Ph.D. thesis, (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, (2005), 5905. 
[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), 609. 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, (2008), 10081. 
[14] 
M. Nakhla and E. Gad, Efficient model reduction of linear timevarying systems via compressed transient system function,, in Conference on Design, (2002), 916. 
[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), 1188. doi: 10.1109/TCSI.2005.846661. 
[16] 
T. Penzl, Algorithms for model reduction of large dynamical systems,, Linear Algebra Appl., 415 (2006), 322. 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, (1998), 96. 
[18] 
J. Phillips, Projectionbased approaches for model reduction of weakly nonlinear timevarying systems,, IEEE Trans. ComputerAided Design, 22 (2003), 171. 
[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, (2015). 
[20] 
J. Roychowdhury, Reducedorder modeling of timevarying systems,, IEEE Control Systems Magazine, 46 (1999), 1273. 
[21] 
J. Roychowdhury, Reducedorder modelling of linear timevarying systems,, in ASPDAC '99. Asia and South Pacific, (1999), 53. 
[22] 
Y. Saad, Overview of Krylov subspace methods with applications to control problems,, in International Symposium MTNS89 on Signal Processing, (1990). 
[23] 
Y. Saad, Iterative Methods for Sparse Linear Systems,, 2nd edition, (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), (2003), 1021. 
[25] 
S. B. Salimbahrami, Structure Preserving Order Reduction of Large Scale Second Order Models,, Ph.D. thesis, (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), 187. 
[28] 
R. Telichevesky, J. White and K. Kundert, Efficient steadystate analysis based on matrixfree Krylovsubspace methods,, in 32rd Design Automation Conference, (1995), 480. 
[29] 
R. Telichevesky, J. White and K. Kundert, Efficient AC and noise analysis of twotone RF circuits,, in 33rd annual Design Automation Conference, (1996), 292. 
[30] 
A. A. Vaidyanathan, Multirate digital filters, filters banks, polyphase networks, and applications: A tutorial,, in IEEE Proceedings, (1990), 56. 
[31] 
E. Wachspress, The ADI Model Problem,, 1995, (). 
[32] 
B. Yang and D. Feng, Efficient finitedifference method for quasiperiodic steadystate and small signal analyses,, in IEEE/ACM International Conference on ComputerAided Design, (2000), 272. 
[33] 
L. Zadeh, Frequency analysis of variable networks,, IEEE Transactions on Circuits and Systems, 38 (1950), 291. 
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