@article{Kahouli2026, 
author = {Omar Kahouli and Sulaiman Almohaimeed and Hamdi Gassara and Lilia El Amraoui and Mohamed Ayari},
title = {Finite-time boundedness of delayed Takagi-Sugeno quasi-one-sided Lipschitz systems},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {22258-22276},
keywords = {time delay, quasi-one-sided Lipschitz nonlinearity, finite-time boundedness, observer-based controller},
url = {https://www.sciopen.com/article/10.3934/math.2026901},
doi = {10.3934/math.2026901},
abstract = {This paper investigates the finite-time boundedness (FBss) of perturbed nonlinear systems with interval time-varying delay. First, the system's nonlinear dynamics are represented by a Takagi–Sugeno (TS) fuzzy model, while quasi-one-sided Lipschitz (QL) terms account for either intrinsic nonlinearities or lumped uncertainties. This formulation captures a broad class of systems, encompassing both natural system nonlinearities and aggregated perturbations. Second, to ensure the FBss of the proposed system, an observer-based controller (OC) is employed under the assumption that the premise variables are measurable, even if the QL condition itself involves unmeasurable states. Then, a single-step procedure based on linear matrix inequalities (LMIs) is proposed to design the OC gains. To this end, a Lyapunov–Krasovskii (LK) functional is employed, comprising a delay-free quadratic term, which incorporates the matrix        P   used to verify the QL condition, along with three integral terms that capture the effects of the interval time-varying delay, including its lower and upper bounds. In addition, we employ a suitable decoupling approach that allows        P   to be regarded as a full decision-variable matrix and enabling the LMI conditions to be derived in a single step. The effectiveness and feasibility of the proposed methods are finally verified through a simulation study.}
}