State and unknown inputs estimation for Takagi–Sugeno systems with immeasurable premise variables: Proportional Multiple Integral observer design

Abstract

In this work, we focus on the design of a Proportional Multiple Integral (PMI) observer for Takagi–Sugeno (T–S) fuzzy systems with immeasurable premise variables subjected to unknown inputs. The LMI-based stability conditions are significantly relaxed by the introduction of an output error injection in the premise variable of the PMI observer. The efficiency of the proposed observer is finally illustrated by a simulation example of a chaotic system.