A comparative view to H_infinity-norm of transfer functions of linear DAEs

Hasan Gündüz; Ercan Çelik; Mesut Karabacak

doi:10.11121/ijocta.1575

Authors

Hasan Gündüz Department of Mathematics, Bingol University, Türkiye https://orcid.org/0000-0001-5851-3819
Ercan Çelik Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Kyrgyzstan https://orcid.org/0000-0002-1402-1457
Mesut Karabacak Department of Mathematics, Ataturk University, Türkiye https://orcid.org/0000-0002-0057-8115

DOI:

https://doi.org/10.11121/ijocta.1575

Keywords:

DAEs systems, H_∞-norm, Bisection method, Extended balanced singular perturbation method

Abstract

In this paper, bisection and extended-balanced singular perturbation methods are used to calculate the H_infinity-norm of the transfer function of a linear DAEs system for the particular case D=0. In the beginning, the approaches' algorithms and error analysis are provided separately. Next, the methods are employed to calculate the H_infinity-norms of a numerical example pertaining to an automotive gas turbine model, and the error limits are used to check the norms in the suitable range, respectively. Ultimately, every solution is compared individually with the problem's H_infinity-norm values, which are retrieved from MATLAB.

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Author Biographies

Hasan Gündüz, Department of Mathematics, Bingol University, Türkiye

Hasan Gunduz is an assistant professor at Bingol University. He received his PhD in applied mathematics from Ataturk University in 2023. His research interests include differential algebraic equations (DAEs), control systems, optimization, numerical analysis.

Ercan Çelik, Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Kyrgyzstan

Ercan Çelik obtained his PhD degree in mathematics at Ataturk University, Erzurum, Turkey in 2002. He is currently working as a professor at the Department of Mathematics, Kyrgyz-Turkish Manas University, Kyrgyzstan. His fields of research are optimization, numerical analysis, and applied mathematics.

Mesut Karabacak, Department of Mathematics, Ataturk University, Türkiye

Mesut Karabacak is an associate professor in the Department of Mathematics at Ataturk University, Erzurum, Turkey. He holds a PhD in Applied Mathematics (2015) from the same university. His research interests are in numerical analysis, wavelet theory, fractional partial differential equations (PDEs), and information theory.

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