This paper addresses the state and sensor fault estimation for nonlinear systems represented by Takagi-Sugeno (T-S) models. The considered faults are time-varying and with multiplicative effect on the sensor output signals. The proposed estimation procedure is based firstly on the sector nonlinearity approach using the convex polytopic transformation where the original system is equivalently rewritten as a Takagi-Sugeno system with unmeasurable premise variables and, secondly on the design of

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... observer allowing the fault estimation by solving an LMI optimization problem. An application of the proposed approach to a simplified model of an activated sludge reactor model is proposed.