Unknown Dynamics Decoupling to Overcome Unmeasurable Premise Variables in Takagi–Sugeno Observer Design

This letter discusses a new approach to overcome unmeasurable premise variables in observer synthesis for Takagi-Sugeno models. The main idea is based on the decoupling of the nonlinear dynamics in order to manage unmeasured state existing into the membership functions. The obtained structure is a system with membership functions subjected only to measured variables. The stability analysis of the observer is carried out using Lyapunov theory. The observer gains were computed from the resolution of the Linear Matrix Inequality constraints. The present result alleviates the strong conditions assumed in the design of observers for TS systems with unmeasurable premise variables. Simulation results are provided to demonstrate the effectiveness of the proposed approach.