Robust observer synthesis for the uncertain large-scale T–S fuzzy system

This work studies a new method to synthesise a robust observer to estimate the immeasurable state variables for an uncertain large-scale Takagi–Sugeno (T–S) fuzzy system, which has not been considered in the previous studies. This system consists of a set of T–S fuzzy subsystems that are interconnected, but these systems have certain uncertainties. An observer relying on the unknown input method is synthesised such that not only the unknown states are estimated but also the effects of the uncertainties are eliminated completely, even though the upper bounds of the uncertainties are not known. The conditions to design the observer are obtained in the main theorems by employing Lyapunov methodology, S-procedure, and linear matrix inequalities technique. Finally, the illustrative examples are provided to illustrate the advantages and success of the proposed method.