Motivated by the recent progress in Finite-Time Fault Estimation (FTFE) and its application to very few classes of Nonlinear Dynamical Systems (NDSs), this paper aims to drive further advancements in the field. In this research direction, a review of the literature reveals that most studies integrate the Linear Matrix Inequality (LMI) approach with the Takagi–Sugeno fuzzy (TSF) models to approximate nonlinear dynamics. However, the Sum Of Squares (SOS) approach offers numerous advancements and improvements over the LMI approach for TSF models. As an initial effort, by applying the SOS approach, this paper proposes two design procedures to ensure the finite-time boundedness of the state and actuator estimation errors for a class of polynomial fuzzy (PF) models. The first result relies on a polynomial integral observer. The second result is derived using a polynomial proportional-integral observer. Simulation results are provided to compare the two design procedures.
Dhahri et al. (2026) studied this question.