The paper introduces fuzzy observer-based control for rotary inverted pendulum systems, renowned for their inherent instability and complexity. We leverage the Takagi-Sugeno (T-S) fuzzy model, which involves the incorporation of local linear models described by fuzzy rules, thus enabling precise and stable control. The Takagi-Sugeno (T-S) fuzzy model, a versatile framework renowned for its suitability in complex control systems, is central to our approach. The significance of observers in accurately estimating unmeasurable states is underlined, with a focus on elucidating the theoretical foundations of fuzzy observers and their role in bolstering control robustness. Additionally, we introduce the integration of Linear Matrix Inequalities (LMIs) and Parallel Distributed Compensation (PDC) for efficient determination of observer and control gains. These advanced tools work in tandem to empower T-S observer control, ensuring both precision and robustness. This paper shows the potential of fuzzy observer-based control and achieving stability and high-performance control of rotary inverted pendulum systems. The effectiveness of the proposed method is validated through simulation results.
