Synthesis of a unknown inputs proportional integral observer for TS fuzzy models

In this paper, synthesis conditions of a proportional integral observer for a Takagi-Sugeno (TS) fuzzy models subject to unknown inputs and unmeasurable decision variables are established. These unknown inputs affect both state and output of the system. The synthesis of this observer is based on hypothesis that the unknown inputs are under the polynomials form with bounded norm of their k^th derivatives. The Lyapunov theory and L₂-gain technique are used to develop the stability conditions of such observers in LMIs formulation. A numerical example is proposed to validate the proposed design conditions.