Observer-Based Exponential Stabilization for Time Delay Takagi–Sugeno–Lipschitz Models

Omar Kahouli (), Hamdi Gassara, Lilia El Amraoui and Mohamed Ayari
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Omar Kahouli: Department of Electronics Engineering, Applied College, University of Ha’il, Ha’il 2440, Saudi Arabia
Hamdi Gassara: Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering, National School of Engineering of Sfax, University of Sfax, PB 1173, Sfax 3038, Tunisia
Lilia El Amraoui: Department of Electrical Engineering, College of Engineering, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mohamed Ayari: Department of Information Technology, Faculty of Computing and Information Technology, Northern Border University, Arar 91431, Saudi Arabia

Mathematics, 2025, vol. 13, issue 19, 1-13

Abstract: This paper addresses the problem of observer-based control (OBC) for nonlinear systems with time delay (TD). A novel hybrid modeling framework for nonlinear TD systems is first introduced by synergistically combining TD Takagi–Sugeno (TDTS) fuzzy and Lipschitz approaches. The proposed methodology broadens the range of representable systems by enabling Lipschitz nonlinearities to fulfill dual functions: they may describe essential dynamic behaviors of the system or represent aggregated uncertainties, depending on the specific application. The proposed TDTS–Lipschitz (TDTSL) model class features measurable premise variables while accommodating Lipschitz nonlinearities that may depend on unmeasurable system states. Then, through the construction of an appropriate Lyapunov–Krasovskii (L-K) functional, we derive sufficient conditions to ensure exponential stability of the augmented closed-loop model. Subsequently, through a decoupling methodology, these stability conditions are reformulated as a set of linear matrix inequalities (LMIs). Finally, the proposed OBC design is validated through application to a continuous stirred tank reactor (CSTR) with lumped uncertainties.

Keywords: observer-based control; LMIs; Takagi–Sugeno fuzzy model; Lipschitz condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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