KaydedilenlerDerginizi ekleyin

Dergiler / Gazi University Journal of Science / 2026 / Volume: 38 Issue: 1

H∞-Norm Evaluation of Transfer Matrices of Dynamical Systems via Extended Balanced Singular Perturbation Method

Hasan Gündüz(BİNGÖL ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0001-5851-3819
Mesut Karabacak(ATATURK UNIVERSITY)0000-0002-0057-8115
Ercan Celık(KYRGYZ - TURKISH MANAS UNIVERSITY)0000-0001-5971-7653
Sayfa
—
Yayın Tarihi
2025-03-01
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The method is then applied to a decentralized interconnected system, and the error analysis of the solution is investigated.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we use a hybrid approach known as the extended balanced singular perturbation technique to compute the H_∞-norm of a transfer matrix of a dynamical system.
📊
Temel Bulgular & Veri:The transfer matrix's order is first reduced using the balanced truncation approach, and its H_∞-norm is then found using the singular perturbation method.
💡
Sonuç & Katkı:The method is then applied to a decentralized interconnected system, and the error analysis of the solution is investigated.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:H∞-control · Balanced truncation approach · Model order reduction

Abstract

In this paper, we use a hybrid approach known as the extended balanced singular perturbation technique to compute the H_∞-norm of a transfer matrix of a dynamical system. The transfer matrix's order is first reduced using the balanced truncation approach, and its H_∞-norm is then found using the singular perturbation method. Both the singular perturbation technique and the balanced truncation approach methods are provided with computer algebraic instructions. The method is then applied to a decentralized interconnected system, and the error analysis of the solution is investigated.

🔖

Bu Makaleye Atıf Yap

Gündüz, H., Karabacak, M., Celık, E. (2025). H∞-Norm Evaluation of Transfer Matrices of Dynamical Systems via Extended Balanced Singular Perturbation Method. Gazi University Journal of Science, Volume: 38 Issue: 1. https://doi.org/10.35378/gujs.1461292

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (19)

  1. Zames, G., “Feedback and optimal sensitivity: Model reference transformations, Multiplicative seminorms and approximate inverses”, IEEE Transactions on Automatic Control, 26(2): 301-20, (1981).
  2. Boyd, S., Balakrishnan, V., Kamamba, P., “A bisection method for computing the H_∞-norm of a transfer matrix and related problems”, Mathematics of Control, Signals and Systems, 2(3): 207-19, (1989).
  3. Kuster, G. E., “H-infinity norm calculation via a state-space formulization”, Master Thesis Faculty of the Virginia Polytechnique Institute and State University, (2012).
  4. Gunduz, H., Celik. E., “H_∞-norm evaluation for a transfer matrix via bisection algorithm”, Thermal Science, 26 (2): 745-51, (2022).
  5. Bruinsma, N. A., Steinbuch, M., “A fast algorithm to compute the H_∞-norm of a transfer function matrix”, System and Control Letters, 14(4): 287-93, (1990).
  6. James, D., Kresimir. V., “Jacobi's method is more accurate than QR”, Computer Science Department Technology Reports, Courant Institute, New York, (1989).
  7. Haider, S., Ghafoor, A., Imran, M., Mumtaz, F., “Techniques for computation of frequency limited H_∞-norm”, IOP Conference Series: Earth and Environmental Science, 114: 012-013, (2018).
  8. Liu, Y., Anderson, B., “Singular perturbation approximation of balanced systems”, International Journal of Control, 50: 1379-1405, (1989).
  9. Suman, S. K., Kumar, A., “A reduction of large-scale dynamical systems by extended balanced singular perturbation approximation”, International Journal of Mathematical, Engineering and Management Sciences, 5(5): 939-56, (2020).
  10. Gajic, Z., Lelic, M., “Improvement of system order reduction via balancing using the method of singular perturbations”, Automatica, 37(11): 1859-65, (2001).
  11. Moore, B., “Principal component analysis in linear systems: Controllability, observability and model reduction”, IEEE Transactions on Automatic Control, 26(1): 17-32, (1981).
  12. Pernebo, L., Silverman, L., “Model reduction via balanced state-space representations”, Institute of Electrical and Electronic Engineering Transactions on Automatic Control, 27(2): 382-87, (1989).
  13. Enns, D. F., “Model reduction with balanced realization: An error bound and a frequency weighted generalization”, The 23rd Institute of Electrical and Electronic Engineering Conference on Decision and Control, 127-32, (1984).
  14. Imran, M, Ghafoor, A, Sreeram, V., “A frequency weighted model order reduction technique and error bounds”, Automatica, 50(12): 3304-3309, (2014).
  15. Kokotovic, P.V., O’Malley, R.E. and Sannuti, P., “Singular perturbations and order reduction in control theory-An overview”, Automatica, 12(2): 123–132, (1976).
  16. N'Diaye, M., Hussain, S., Suliman, I. M. A., Toure, L., “Robust uncertainty alleviation by H-infinity analysis and control for singularity perturbed systems with disturbances”, Journal of Xi'an Shioyu University, Natural Science Edition, 19(01): 728-37, (2023).
  17. Datta, B. N., Numerical methods for linear control systems (1), London, New York. Academic Press, (2004).
  18. Antoulas, A. C., Benner, P., Feng. L., “Model reduction by iterative error system approximation”, Mathematical and Computer Modelling of Dynamical Systems, 24(2): 103–18, (2018).
  19. Saif, M., Guan. Y., “Decentralized state estimation in large-scale interconnected dynamical systems”, Automatica, 28(1): 215-19, (1992).