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Symmetry
Volume 18
Issue 6
10.3390/sym18061014
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

H∞ Control Designs for Continuous-Time Singular Systems

by
Badreddine El Haiek
1,†,
Hicham El Aiss
1,†,
Taha Zoulagh
2,*,† and
Fernando Tadeo
3,*,†
1
Identification and Control Laboratory, Department of Electrical Engineering, University of Santiago of Chile, Santiago 3580000, Chile
2
Euromed University of Fes, UEMF, Fes 30000, Morocco
3
Institute of Sustainable Processes, Universidad de Valladolid, 47002 Valladolid, Spain
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2026, 18(6), 1014; https://doi.org/10.3390/sym18061014 (registering DOI)
Submission received: 21 April 2026 / Revised: 1 June 2026 / Accepted: 8 June 2026 / Published: 12 June 2026
(This article belongs to the Special Issue Symmetry in Fuzzy Systems and Control: A Path to Innovative Solutions)
Versions Notes

Abstract

This paper investigates some H∞ control problems for linear continuous-time singular systems. The objective is to design controllers that guarantee the admissibility of the closed-loop system and simultaneously achieve a prescribed H∞ disturbance attenuation level. To this end, a framework based on novel strict LMIs (Linear Matrix Inequalities) is developed using a Lyapunov function approach for the analysis of admissibility and H∞ performance. In particular, an additional scalar parameter α is introduced to generalize the condition reported in previous results in the literature, providing greater flexibility. Then, sufficient LMI conditions are derived for the synthesis of both state-feedback and static output-feedback controllers. Finally, some numerical examples demonstrate the effectiveness of the proposed method.
Keywords: continuous-timesingular system; state-feedback; output-feedback; H∞ performance; linear matrix inequalities (LMIs); system variability continuous-timesingular system; state-feedback; output-feedback; H∞ performance; linear matrix inequalities (LMIs); system variability

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MDPI and ACS Style

El Haiek, B.; Aiss, H.E.; Zoulagh, T.; Tadeo, F. H∞ Control Designs for Continuous-Time Singular Systems. Symmetry 2026, 18, 1014. https://doi.org/10.3390/sym18061014

AMA Style

El Haiek B, Aiss HE, Zoulagh T, Tadeo F. H∞ Control Designs for Continuous-Time Singular Systems. Symmetry. 2026; 18(6):1014. https://doi.org/10.3390/sym18061014

Chicago/Turabian Style

El Haiek, Badreddine, Hicham El Aiss, Taha Zoulagh, and Fernando Tadeo. 2026. "H∞ Control Designs for Continuous-Time Singular Systems" Symmetry 18, no. 6: 1014. https://doi.org/10.3390/sym18061014

APA Style

El Haiek, B., Aiss, H. E., Zoulagh, T., & Tadeo, F. (2026). H∞ Control Designs for Continuous-Time Singular Systems. Symmetry, 18(6), 1014. https://doi.org/10.3390/sym18061014

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