## 1 Introduction  
Fuzzy logic methods emerged in the mid-1960s with the foundational work presented in [1], where a fuzzy set is defined through a membership function that assigns each element a degree of membership ranging from zero to one. Subsequently, in 1973, [PERSON] expanded on this concept by introducing fuzzy algorithms, which are structured sequencesof instructions formulated through IF-THEN rules [2]. In the same year, the first documented industrial application of fuzzy logic was reported in [3]. This study explored the development of a \"linguistic\" controller for a steam engine model, aiming to analyze human interaction with adaptive control strategies. Unexpectedly, the fuzzy control approach demonstrated superior performance, significantly exceeding expectations and fostering broader interest in the application and advancement of fuzzy logic systems  
The work presented in [4] compares fuzzy control methods with other nonlinear control strategies. It points out that a major drawback of fuzzy control lies in its inability to clearly define a direct link between membership functions and the system's states, an unresolved issue. The authors also suggest that nonlinear control approaches, especially those specifically adapted to the system's structure, often demonstrate superior performance compared to fuzzy techniques. The study presented in [5] focuses on Takagi-Sugeno-Kang (TSK) fuzzy systems, which enable the representation of general nonlinear dynamics through a compact set of rules. This work also introduces a methodology for designing fuzzy controllers capable of ensuring closed-loop stability when using TSK models. A practical implementation of fuzzy control is illustrated in [6], where a fuzzy logic controller is applied to a magnetic levitation system of a metallic sphere. The main contribution lies in the comparative analysis between the fuzzy controller and both linear (PD and PID) and nonlinear alternatives. The results reveal a superior performance of the fuzzy controller, primarily due to its effectiveness in managing the inherent nonlinearities of the system. The research outlined in [7] introduces the well-established Takagi-Sugeno (T-S) identification method for modeling systems based on input-output data. A notable limitation of this method is its inapplicability in scenarios where membership functions exhibit pairwise overlap. To address this shortcoming, the approaches proposed in [8; 9] incorporate parameter weighting to refine the values obtained through standard T-S identification, thereby mitigating the constraints of the original formulation. Furthermore, a Linear Quadratic Regulator (LQR) is employed to evaluate the performance of the proposed estimation framework. Validation through two illustrative examples confirms the robustness, simplicity, and general applicability of the algorithm developed. The study conducted in [10] illustrates the application of modern control theory, rooted in time-domain analysis and state-space modeling, to systems with multiple inputs and outputs, including those exhibiting nonlinear behavior. In this study, the authors address the challenges posed by complex airflow dynamics, noting that few models adequately capture the dynamic distribution of indoor temperature. To improve accuracy in temperature prediction and control, a state-space model is employed and experimentally validated, yielding realistic and reliable results. Similarly, the study in [11] proposes an enhanced aeroservoelastic modeling framework for gust load analysis using time-domain state-space representations. The approach effectively handles the computational complexity of gust calculations and proves advantageous for control system design. A subsystem realization methodology is introduced to construct the full aeroservoelastic model, with simulation results confirming its high predictive accuracy. The contributions presented in [12; 13] demonstrate further applications of the state-space modeling paradigm in control design.