A Decoupling Approach to Design Observers for Polytopic Takagi-Sugeno Models Subject to Unknown Inputs

A decoupling approach for state estimation of nonlinear systems represented in the polytopic Takagi-Sugeno with unmeasurable premise variables subject to unknown inputs is proposed in this paper. The idea consists in defining a state and unknown input transformations in order to divide the state vector into two parts, a measurable part and an observable one (decoupled from the unknown input). A classical Luenberger observer to estimate the unmeasurable part is then designed and given in terms of Linear Matrix Inequalities (LMIs) conditions. A numerical example is also presented in order to illustrate the proposed approach.