A COMPARATIVE EVALUATION OF MODEL ORDER REDUCTION TECHNIQUES FOR FILTER CIRCUITS
Abstract
Filter circuits often yield high-order dynamical models that impose significant computational cost. Model order reduction provides compact surrogate models that preserve dominant input-output behavior while reducing complexity. This paper presents a comparative evaluation of representative Model order reduction techniques for filter circuits, including balanced truncation, stochastic balanced truncation, modal truncation, and positive real balanced truncation. A sixth-order Chebyshev filter model is used as a benchmark. All methods are applied at identical reduced orders and evaluated using H∞ error norms together with time-domain step and impulse responses. The results highlight clear differences in absolute
and relative errors, and step and impulse responses among the considered techniques.
References
B. C. Moore, “Principal component analysis in linear systems: Controllability, observability, and
model reduction,” IEEE Trans. Autom. Control, vol. AC-26, no. 1, pp. 17–32, Feb. 1981.
L. Pernebo and L. M. Silverman, “Model reduction via balanced state space representations,” IEEE
Trans. Autom. Control, vol. AC-27, no. 2, pp. 382–387, Apr. 1982.
A. R. Desai and D. Pal, “A transformation approach to stochastic model reduction,” IEEE Trans.
Autom. Control, vol. AC-29, no. 12, pp. 1097–1100, Dec. 1984.
M. Green, “Balanced stochastic realizations,” Linear Algebra and its Applications, vol. 98, pp. 211
, 1988.
X. Wang and M. G. Safonov, “A tighter relative-error bound for balanced stochastic truncation,”
Automatica, vol. 26, no. 5, pp. 939–943,1990.
R. Ober, “Balanced realization and model reduction of linear systems,” Int. J. Control, vol. 54, no.
, pp. 1–43, 1991.
A. Varga and K. H. Fasol, “A new square-root balancing-free stochastic truncation model reduction
algorithm,” Prepr. 12th IFACWorld Congress, vol. 7, pp. 153–156, 1993.
K. Zhou, J. C. Doyle, and K. Glover, “Robust and Optimal Control”. Englewood Cliffs, NJ: Prentice
Hall, 1996.
A. Varga, “On stochastic balancing related model reduction,” in Proc. 39th IEEE Conf. Decision and
Control (CDC), Sydney, Australia, 2000, pp. 3503–3508.
P. Benner, E. S. Quintana-Ort´ı, and G. Quintana-Ort´ı, “Efficient numerical algorithms for balanced
stochastic truncation,” Int. J. Appl.Math. Comput. Sci., vol. 11, no. 5, pp. 1123–1150, 2001.
S. Gugercin and A. C. Antoulas, “A survey of model reduction by balanced truncation and some new
results,” Int. J. Control, vol. 77, no. 8, pp. 748–766, May 2004.
S. Gugercin, A. C. Antoulas, and C. Beattie, “Rational Krylov methods for optimal H2 model
reduction,” Proceedings of the 45th IEEE Conference on Decision and Control (CDC), San Diego,
CA, USA, pp. 2832–2837, Dec. 2006.
S. Gugercin, A. C. Antoulas, and C. Beattie, “H2 model reduction for large-scale linear dynamical
systems,” SIAM J. Matrix Anal. Appl., vol. 30, no. 2, pp. 609–638, 2008.
G. M. Flagg, C. Beattie, and S. Gugercin, “Convergence of the iterative rational Krylov algorithm,”
Syst. Control Lett., vol. 61, no. 1, pp. 122–129, 2012.
B. T. Thanh, “Model order reduction based on Schur analysis for two-wheeled balanced robot
control,” Vietnam J. Mech. Eng., no. 9, pp. 45–52, 2014.
T. Damm and P. Benner, “Balanced truncation for stochastic linear systems with guaranteed error
bound,” in Proc. 21st Int. Symp. Mathematical Theory of Networks and Systems (MTNS), Groningen,
Netherlands, 2014, pp. 1498–1505.
A. Semlyen, A. Ramirez, B. Gustavsen, and R. Iravani, “Dominant modes identification of linear
systems via geometrical search,” IEEE Transactions on Power Delivery, vol. 36, no. 6, pp. 3289
, 2020.
H.-D. Dao, T.-T. Nguyen, N.-K. Vu, H.-M. Viet, H.-V. Ta, and T.-V. Phuong, “Developing new
model order reduction algorithms toenhance the efficiency of large-scale electrical and electronic
circuit simulation: Mixed Balanced Truncation and Riccati–Lyapunov Mixed Balanced Truncation,”
J. Mech. Sci. Technol., vol. 101, no. 101, pp. 13–22, Feb. 2025. doi: 10.54939/1859-1043.j.m
st.101.2025.13-22.
T.-T. Nguyen et al., “Efficient simulation of large-scale electrical circuits with mixed balanced
truncation algorithm,” Int. J. Control, Autom. Syst., vol. 23, no. 4, pp. 1035–1045, 2025.
A. C. Antoulas and I. V. Gosea, “Data-driven model reduction for weakly nonlinear systems: A
summary,” IFAC-PapersOnLine, vol. 48, no. 1, pp. 3–4, 2015.
Freitas, F.D., Rommes, J., Martins, N. , “Developments in the Computation of Reduced Order Models
with the Use of Dominant Spectral Zeros,” Realization and Model Reduction of Dynamical Systems.
Springer, Cham, 2022. https://doi.org/10.1007/978-3-030-95157-3_12
S. Reiter, I. V. Gosea, and S. Gugercin, “Generalizations of data-driven balancing: What to sample for
different balancing-based reduced models,” Automatica, vol. 182, 112518, 2025.
P. Prommee, P. Thongdit, and K. Angkeaw, “Log-domain high-order low-pass and band-pass filters,”
AEU – International Journal of Electronics and Communications, vol. 79, pp. 234–242, Sep. 2017.
H. R. Ali, L. P. Kunjumuhammed, B. C. Pal, A. G. Adamczyk, and K. Vershinin, “Model order
reduction of wind farms: Linear approach,” IEEE Transactions on Sustainable Energy, vol. 10, no.
, pp. 1194–1205, 2018.
D.-T. Vu, H.-D. Dao, N.-K. Vu, T.-N. Vu, and T.-T. Nguyen, “Model order reduction techniques for
large-scale electrical networks: A comparative study,” in Advances in Information and Communication
Technology, Springer, 2025, pp. 863–874.
P. Vuillemin, A. Maillard, and C. Poussot-Vassal, “Optimal modal truncation,” Systems & Control
Letters, vol. 156, Art. no. 105011, 2021.
