Simplified LMI Conditions for Takagi-Sugeno Fuzzy Observer Design with Unmeasured Premise Variables

This article introduces a method that simplifies the process of designing an observer for Takagi-Sugeno (T-S) fuzzy models with unmeasured premise variables. By incorporating an adjustment parameter into the simplified Linear Matrix Inequality (sLMI) conditions, the dynamic error of the system can be controlled to remain within a specified region, ensuring better system performance. Through a basic linear algebra analysis, the relationship between the system’s membership functions and the estimated ones is established. Lyapunov’s theorem is employed to formulate the sLMI condition. Additionally, to optimize the sLMI conditions with the aim of minimizing dynamic error, an optimization problem is formulated. Finally, numerical simulations were executed on the Rotary Inverted Pendulum (RIP) system to validate the proposed control approach.