## 1 Introduction
[PERSON] [12] incorporates the model within a model predictive control framework, whereas [13] utilizes it for the regulation of a four-tank process. In the latter study, as is common in system identification tasks, the derivation of accurate models typically requires full knowledge of both input and output signals. However, when one or more inputs are partially unknown, the identification process becomes significantly more challenging or even infeasible. To address this limitation, the methodology proposed in [14] introduces an iterative estimation procedure capable of reconstructing the system state trajectory and inferring the unknown input signal based solely on output measurements. This technique effectively mitigates one of the primary obstacles associated with conventional identification approaches. The control strategy outlined in [15] leverages the incremental state-space model to achieve zero steady-state error in response to step-type reference signals. This formulation is further employed in [16] for the optimal multivariable control of a wind turbine system. The evaluation involves the application of Linear Quadratic Regulator (LQR) controllers to a nonlinear wind turbine model, with simulation results indicating favorable transient performance and complete steady-state error rejection, even in the presence of external disturbances, nonlinearities, and model inaccuracies. The work in [17] reinforces the suitability of the incremental modeling approach for addressing the intrinsic nonlinearity and uncertainty of the plant. Additional findings in [18] demonstrate that incremental control strategies can effectively resolve continuous-time nonlinear control problems without requiring a comprehensive global model of the system. The foundational work in [19] demonstrates that the state vector of a linear system can be reconstructed by monitoring the system's inputs and outputs. This study introduces the concept of a state observer, which enables estimation of the system's internal states when direct measurement is impractical--a common scenario in real-world control applications. The relevance of this methodology is further substantiated in [20; 21], where state observers are employed to estimate the system states and facilitate the design of optimal state-feedback controllers. Simulation analyses presented in both references validate the proposed approaches, highlighting their ability to ensure global stability and accurate state estimation. The comparative study conducted in [22] analyzes the performance of three advanced state observers: high-gain, sliding mode, and extended state observers developed to address the inherent limitations of classical observer designs. The results indicate that the extended state observer outperforms the others in terms of robustness to dynamic uncertainties, sensor noise, and external disturbances. A similar evaluation is presented in [23], where the Luenberger estimator, Kalman filter, and sliding mode observer are assessed for estimating the speed of a DC motor. The findings underscore that observer performance is highly dependent on the specific characteristics of the system, with each method exhibiting distinct advantages under different operational conditions. The Linear Quadratic Regulator (LQR) has been widely adopted in state-space control for both continuous- and discrete-time systems due to its inherent robustness and optimal performance characteristics. [PERSON] [24] employs the LQR to demonstrate its ability to ensure system stability under predefined conditions, even in the presence of actuator faults and significant external disturbances. A complementary study is presented in [25], where the LQR is integrated into a fuzzy control architecture. In this case, the nonlinear system is linearized using the Lyapunov linearization technique and modeled through the Takagi-Sugeno (T-S) fuzzy framework. This representation enables the implementation of an LQR controller within each locally linearized region.