Design of a Functional Observer for Fuzzy Delayed Systems with Unknown Input

This study focuses on the design of observers with unknown inputs for delayed systems represented by Takagi-Sugeno (T-S) in continuous time. When the unknown inputs are included in the state and output equations, and the delays are assumed to be bounded, fuzzy functional observers are derived. The design and analysis of the observer is based on Lyapunov-Krasovskii stability theory, and the convergence conditions of the observer are expressed in terms of linear matrix inequalities (LMIs), which can be solved numerically and symbolically using the LMI or YALMIP toolboxes. In the last part of the paper, a detailed example is proposed to prove the applicability of this technique.