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Article

Linear Algebra-Based Multivariable Controller Design for Gas Turbine Machines with State-Derivative Feedback

by
Belkacem Bekhiti
1,
Kamel Hariche
2,
Abderrezak Guessoum
3 and
Abdel-Nasser Sharkawy
4,5,*
1
Institute of Aeronautics and Space Studies, (IASS), University of Blida 1, BP 270, Blida 09000, Algeria
2
Institute of Electrical and Electronic Engineering (IGEE), University of Boumerdes, Boumerdes 35000, Algeria
3
Signal Processing and Image Laboratory (LATSI), Department of Electronics, Faculty of Technology, University of Blida, Blida 09000, Algeria
4
Mechanical Engineering Department, Faculty of Engineering, Qena University, Qena 83523, Egypt
5
Mechanical Engineering Department, College of Engineering, Fahad Bin Sultan University, Tabuk 47721, Saudi Arabia
*
Author to whom correspondence should be addressed.
Machines 2026, 14(2), 169; https://doi.org/10.3390/machines14020169
Submission received: 31 December 2025 / Revised: 24 January 2026 / Accepted: 27 January 2026 / Published: 2 February 2026
(This article belongs to the Section Automation and Control Systems)

Abstract

This paper presents a linear algebra-based control algorithm for multivariable gas turbine systems using matrix polynomial theory and the Kronecker product to assign block roots (i.e., block eigenvectors with prescribed latent structure). State and state-derivative feedback strategies are investigated and validated through simulations on an industrial gas turbine machine. The proposed method enables direct assignment of block roots governing closed-loop stability and transient response, while block eigenvectors shape the dynamic behavior of key turbine variables. Applicability of the approach requires block controllability and/or block observability, ensuring analytical transparency, design flexibility, and effectiveness for multivariable gas turbine control.
Keywords: state-derivative feedback; block-roots; block-eigenvectors; latent structure; matrix polynomial; Kronecker product state-derivative feedback; block-roots; block-eigenvectors; latent structure; matrix polynomial; Kronecker product

Share and Cite

MDPI and ACS Style

Bekhiti, B.; Hariche, K.; Guessoum, A.; Sharkawy, A.-N. Linear Algebra-Based Multivariable Controller Design for Gas Turbine Machines with State-Derivative Feedback. Machines 2026, 14, 169. https://doi.org/10.3390/machines14020169

AMA Style

Bekhiti B, Hariche K, Guessoum A, Sharkawy A-N. Linear Algebra-Based Multivariable Controller Design for Gas Turbine Machines with State-Derivative Feedback. Machines. 2026; 14(2):169. https://doi.org/10.3390/machines14020169

Chicago/Turabian Style

Bekhiti, Belkacem, Kamel Hariche, Abderrezak Guessoum, and Abdel-Nasser Sharkawy. 2026. "Linear Algebra-Based Multivariable Controller Design for Gas Turbine Machines with State-Derivative Feedback" Machines 14, no. 2: 169. https://doi.org/10.3390/machines14020169

APA Style

Bekhiti, B., Hariche, K., Guessoum, A., & Sharkawy, A.-N. (2026). Linear Algebra-Based Multivariable Controller Design for Gas Turbine Machines with State-Derivative Feedback. Machines, 14(2), 169. https://doi.org/10.3390/machines14020169

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