Design of multiobserver for nonlinear systems represented by fuzzy T–S models with sensor faults

Abstract

This paper deals with the estimation of sensor faults for nonlinear systems represented by a Takagi–Sugeno (T–S) fuzzy model. The basic idea is to introduce an augmented state vector which groups together the states of the fuzzy T–S model and the sensor faults. In order to ensure the robustness of the proposed multiobserver and guarantee the convergence conditions, analysis and stability study are based on the candidate Lyapunov function and the formulation of Linear Matrix Inequality (LMI). The impact of the derivation of sensor faults has been attenuated using the $$H_{\infty }$$ performance in the proposed multiobserver. To illustrate the validation of this observer, an academic example will be introduced in this work.