-
Previous Article
A new computational strategy for optimal control problem with a cost on changing control
- NACO Home
- This Issue
-
Next Article
Decentralized gradient algorithm for solution of a linear equation
Partial fraction expansion based frequency weighted model reduction for discrete-time systems
1. | Motilal Nehru National Institute of Technology Allahabad, Allahabad, Uttar Pradesh 211004, India |
2. | School of Electrical and Electronics Engineering, University of Western Australia, 35 Stirling Highway, WA 6009, Australia, Australia |
References:
[1] |
D. W. Ding, X. Du and X. Li, Finite-frequency model reduction of two-dimensional digital filters, IEEE Trans. Autom. Control, 60 (2015), 1624-1629.
doi: 10.1109/TAC.2014.2359305. |
[2] |
X. Du, F. Fan, D. W. Ding and F. Liu, Finite-frequency model order reduction of discrete-time linear time-delayed systems, Nonlinear Dynamics, 83 (2016), 2485-2496.
doi: 10.1007/s11071-015-2496-0. |
[3] |
D. Enns, Model reduction with balanced realizations: An error bound and a frequency weighted generalization, In: Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, USA, (1984), 127-132. |
[4] |
M. Imran and A. Ghafoor, Model reduction of descriptor systems using frequency limited gramians, J. Franklin Inst., 352 (2015), 33-51.
doi: 10.1016/j.jfranklin.2014.10.013. |
[5] |
X. Li, C. Yu and H. Gao, Frequency limited H∞ model reduction for positive systems, IEEE Trans. Autom. Control, 60 (2015), 1093-1098.
doi: 10.1109/TAC.2014.2352751. |
[6] |
C. A. Lin and T. Y. Chiu, Model reduction via frequency weighted balanced realization, Control Theory and Advanced Technology, 8 (1992), 341-451. |
[7] |
Y. Liu and B. D. O. Anderson, Singular perturbation approximation of balanced systems, International Journal of Control, 50 (1989), 1339-1405.
doi: 10.1080/00207178908953437. |
[8] |
B. C. Moore, Principal component analysis in linear system: Controllability, observability, and model reduction, IEEE Trans. Automat. Contr, AC-26 (1981), 17-32.
doi: 10.1109/TAC.1981.1102568. |
[9] |
U. M. Saggaf and G. F. Franklin, On model reduction, Proc. of the 23rd IEEE Conf. on Decision and Control, (1986), 1064-1069. |
[10] |
U. M. Saggaf and G. F. Franklin, Model reduction via balanced realization, IEEE Trans. on Autom. Control, AC-33 (1988), 687-692.
doi: 10.1109/9.1280. |
[11] |
H. R. Shaker and M. Tahavori, Frequency interval model reduction of bilinear systems, IEEE Trans. Autom. Control, 59 (2014), 1948-1953.
doi: 10.1109/TAC.2013.2295661. |
[12] |
V. Sreeram and B. D. O. Anderson, Frequency weighted balanced reduction technique: A generalization and an error bound, Proceedings of the 34th IEEE Conference on Decision and Control, (1995), 3576-3581. |
[13] |
V. Sreeram, S. Sahlan, W. M. W Muda, T. Fernando and H. H. C. Iu, A generalised partial-fraction-expansion based frequency weighted balanced truncation technique, International Journal of Control, 86 (2013), 833-843.
doi: 10.1080/00207179.2013.764017. |
[14] |
T. Van-Gestel, B. Anderson and P. Van-Overschee, On frequency weighted balanced truncation: Hankel singular values and error bounds, European Journal of Control, 7 (2001), 584-592. |
[15] |
G. Wang, V. Sreeram and W. Q. Liu, A new frequency-weighted balanced truncation method and an error bound, IEEE Transactions on Automatic Control, 44 (1999), 1734-1737.
doi: 10.1109/9.788542. |
show all references
References:
[1] |
D. W. Ding, X. Du and X. Li, Finite-frequency model reduction of two-dimensional digital filters, IEEE Trans. Autom. Control, 60 (2015), 1624-1629.
doi: 10.1109/TAC.2014.2359305. |
[2] |
X. Du, F. Fan, D. W. Ding and F. Liu, Finite-frequency model order reduction of discrete-time linear time-delayed systems, Nonlinear Dynamics, 83 (2016), 2485-2496.
doi: 10.1007/s11071-015-2496-0. |
[3] |
D. Enns, Model reduction with balanced realizations: An error bound and a frequency weighted generalization, In: Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, USA, (1984), 127-132. |
[4] |
M. Imran and A. Ghafoor, Model reduction of descriptor systems using frequency limited gramians, J. Franklin Inst., 352 (2015), 33-51.
doi: 10.1016/j.jfranklin.2014.10.013. |
[5] |
X. Li, C. Yu and H. Gao, Frequency limited H∞ model reduction for positive systems, IEEE Trans. Autom. Control, 60 (2015), 1093-1098.
doi: 10.1109/TAC.2014.2352751. |
[6] |
C. A. Lin and T. Y. Chiu, Model reduction via frequency weighted balanced realization, Control Theory and Advanced Technology, 8 (1992), 341-451. |
[7] |
Y. Liu and B. D. O. Anderson, Singular perturbation approximation of balanced systems, International Journal of Control, 50 (1989), 1339-1405.
doi: 10.1080/00207178908953437. |
[8] |
B. C. Moore, Principal component analysis in linear system: Controllability, observability, and model reduction, IEEE Trans. Automat. Contr, AC-26 (1981), 17-32.
doi: 10.1109/TAC.1981.1102568. |
[9] |
U. M. Saggaf and G. F. Franklin, On model reduction, Proc. of the 23rd IEEE Conf. on Decision and Control, (1986), 1064-1069. |
[10] |
U. M. Saggaf and G. F. Franklin, Model reduction via balanced realization, IEEE Trans. on Autom. Control, AC-33 (1988), 687-692.
doi: 10.1109/9.1280. |
[11] |
H. R. Shaker and M. Tahavori, Frequency interval model reduction of bilinear systems, IEEE Trans. Autom. Control, 59 (2014), 1948-1953.
doi: 10.1109/TAC.2013.2295661. |
[12] |
V. Sreeram and B. D. O. Anderson, Frequency weighted balanced reduction technique: A generalization and an error bound, Proceedings of the 34th IEEE Conference on Decision and Control, (1995), 3576-3581. |
[13] |
V. Sreeram, S. Sahlan, W. M. W Muda, T. Fernando and H. H. C. Iu, A generalised partial-fraction-expansion based frequency weighted balanced truncation technique, International Journal of Control, 86 (2013), 833-843.
doi: 10.1080/00207179.2013.764017. |
[14] |
T. Van-Gestel, B. Anderson and P. Van-Overschee, On frequency weighted balanced truncation: Hankel singular values and error bounds, European Journal of Control, 7 (2001), 584-592. |
[15] |
G. Wang, V. Sreeram and W. Q. Liu, A new frequency-weighted balanced truncation method and an error bound, IEEE Transactions on Automatic Control, 44 (1999), 1734-1737.
doi: 10.1109/9.788542. |
[1] |
Martin Redmann, Peter Benner. Approximation and model order reduction for second order systems with Levy-noise. Conference Publications, 2015, 2015 (special) : 945-953. doi: 10.3934/proc.2015.0945 |
[2] |
Georg Vossen, Stefan Volkwein. Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 465-485. doi: 10.3934/naco.2012.2.465 |
[3] |
Heting Zhang, Lei Li, Mingxin Wang. Free boundary problems for the local-nonlocal diffusive model with different moving parameters. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022085 |
[4] |
Rua Murray. Approximation error for invariant density calculations. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 535-557. doi: 10.3934/dcds.1998.4.535 |
[5] |
Thierry Paul, Mario Pulvirenti. Asymptotic expansion of the mean-field approximation. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1891-1921. doi: 10.3934/dcds.2019080 |
[6] |
Igor E. Pritsker and Richard S. Varga. Weighted polynomial approximation in the complex plane. Electronic Research Announcements, 1997, 3: 38-44. |
[7] |
Araz Hashemi, George Yin, Le Yi Wang. Sign-error adaptive filtering algorithms involving Markovian parameters. Mathematical Control and Related Fields, 2015, 5 (4) : 781-806. doi: 10.3934/mcrf.2015.5.781 |
[8] |
Andrew Raich. Heat equations and the Weighted $\bar\partial$-problem. Communications on Pure and Applied Analysis, 2012, 11 (3) : 885-909. doi: 10.3934/cpaa.2012.11.885 |
[9] |
Elizabeth Carlson, Joshua Hudson, Adam Larios, Vincent R. Martinez, Eunice Ng, Jared P. Whitehead. Dynamically learning the parameters of a chaotic system using partial observations. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 3809-3839. doi: 10.3934/dcds.2022033 |
[10] |
Jing Li, Panos Stinis. Model reduction for a power grid model. Journal of Computational Dynamics, 2022, 9 (1) : 1-26. doi: 10.3934/jcd.2021019 |
[11] |
Jan Haskovec, Nader Masmoudi, Christian Schmeiser, Mohamed Lazhar Tayeb. The Spherical Harmonics Expansion model coupled to the Poisson equation. Kinetic and Related Models, 2011, 4 (4) : 1063-1079. doi: 10.3934/krm.2011.4.1063 |
[12] |
Sanghoon Kwon, Seonhee Lim. Equidistribution with an error rate and Diophantine approximation over a local field of positive characteristic. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 169-186. doi: 10.3934/dcds.2018008 |
[13] |
L. Dieci, M. S Jolly, Ricardo Rosa, E. S. Van Vleck. Error in approximation of Lyapunov exponents on inertial manifolds: The Kuramoto-Sivashinsky equation. Discrete and Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 555-580. doi: 10.3934/dcdsb.2008.9.555 |
[14] |
Xiu Ye, Shangyou Zhang. A new weak gradient for the stabilizer free weak Galerkin method with polynomial reduction. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4131-4145. doi: 10.3934/dcdsb.2020277 |
[15] |
Scott R. Pope, Laura M. Ellwein, Cheryl L. Zapata, Vera Novak, C. T. Kelley, Mette S. Olufsen. Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences & Engineering, 2009, 6 (1) : 93-115. doi: 10.3934/mbe.2009.6.93 |
[16] |
Houssein Ayoub, Bedreddine Ainseba, Michel Langlais, Rodolphe Thiébaut. Parameters identification for a model of T cell homeostasis. Mathematical Biosciences & Engineering, 2015, 12 (5) : 917-936. doi: 10.3934/mbe.2015.12.917 |
[17] |
Kangbo Bao, Libin Rong, Qimin Zhang. Analysis of a stochastic SIRS model with interval parameters. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4827-4849. doi: 10.3934/dcdsb.2019033 |
[18] |
D. Criaco, M. Dolfin, L. Restuccia. Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 59-73. doi: 10.3934/mbe.2013.10.59 |
[19] |
Matteo Bonforte, Jean Dolbeault, Matteo Muratori, Bruno Nazaret. Weighted fast diffusion equations (Part Ⅱ): Sharp asymptotic rates of convergence in relative error by entropy methods. Kinetic and Related Models, 2017, 10 (1) : 61-91. doi: 10.3934/krm.2017003 |
[20] |
Jules Guillot, Emmanuel Frénod, Pierre Ailliot. Physics informed model error for data assimilation. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022059 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]