<p>This article presents a method for designing a fuzzy observer for a Takagi–Sugeno (TS) fuzzy model with Unmeasured Premise Variables (UPVs). Unlike existing approaches in the literature, which typically address the challenges posed by UPVs through the formulation of LMI conditions for stability analysis, this article proposes a novel method. The approach focuses on constructing a membership function to overcome the challenges of UPVs, providing an alternative to finding pairs of controller and observer gains that ensure the overall system’s stability. Based on the separation principle, the controller and observer can be independently designed using LMI conditions. To ensure the stability of the overall system, an appropriate set of membership functions is determined by establishing bounds on the parameters of the new membership functions. Moreover, the reconstructed membership function information is utilized to formulate LMI conditions for stability analysis. Besides that, by using membership function reconstruction, the system also achieves the ability to handle some uncertainties at certain levels. Finally, numerical simulations with the Rotary Inverted Pendulum (RIP) are conducted to validate the effectiveness of the proposed method.</p>

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Reconstructing Membership Functions for Observer-Based Controller Design of Takagi–Sugeno Fuzzy Model with Unmeasured Premise Variables

  • Bao-Trung Dong,
  • Thi-Van-Anh Nguyen

摘要

This article presents a method for designing a fuzzy observer for a Takagi–Sugeno (TS) fuzzy model with Unmeasured Premise Variables (UPVs). Unlike existing approaches in the literature, which typically address the challenges posed by UPVs through the formulation of LMI conditions for stability analysis, this article proposes a novel method. The approach focuses on constructing a membership function to overcome the challenges of UPVs, providing an alternative to finding pairs of controller and observer gains that ensure the overall system’s stability. Based on the separation principle, the controller and observer can be independently designed using LMI conditions. To ensure the stability of the overall system, an appropriate set of membership functions is determined by establishing bounds on the parameters of the new membership functions. Moreover, the reconstructed membership function information is utilized to formulate LMI conditions for stability analysis. Besides that, by using membership function reconstruction, the system also achieves the ability to handle some uncertainties at certain levels. Finally, numerical simulations with the Rotary Inverted Pendulum (RIP) are conducted to validate the effectiveness of the proposed method.