Observer Design for RIP Stability Using Takagi-Sugeno Fuzzy Model and Mean Value Theorem

Quy-Thinh  Dao; Bao-Trung  Dong; Thi-Van-Anh  Nguyen

doi:10.6180/jase.202509_28(9).0019

Observer Design for RIP Stability Using Takagi-Sugeno Fuzzy Model and Mean Value Theorem

Quy-Thinh Dao, Bao-Trung Dong, and Thi-Van-Anh NguyenThis email address is being protected from spambots. You need JavaScript enabled to view it.

School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi 100000, Vietnam

Received: July 4, 2024
Accepted: November 5, 2024
Publication Date: January 13, 2025

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202509_28(9).0019

This paper presents an observer design for the Rotary Inverted Pendulum (RIP) system using the Takagi-Sugeno (T-S) fuzzy model and the mean value theorem. The proposed method addresses the nonlinear and inherently unstable dynamics of the RIP by transforming the error dynamics into a linear parametric varying system. A non-quadratic Lyapunov function candidate is employed to ensure the global exponential convergence of the estimation error to zero. By combining the differential mean value theorem with sector nonlinearity transformation, the observer guarantees robust performance in the presence of unmeasured premise variables. The stability conditions are derived based on the Lyapunov function, leading to the solvability of a set of linear matrix inequalities. Simulation results demonstrate the effectiveness of the proposed observer in significantly reducing dynamic errors and enhancing the overall stability and accuracy of state estimations. The proposed approach outperforms traditional methods, providing a reliable and precise solution for real-time control applications in nonlinear systems.

Keywords: Observer Design; Takagi-Sugeno Fuzzy Model; Stability control; Mean Value Theorem; Rotary Inverted Pendulum

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