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Journals / 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
Pages
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Publication Date
2025-03-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:The method is then applied to a decentralized interconnected system, and the error analysis of the solution is investigated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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.

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Cite This Article

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

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