Robust Fault Detection and Estimation for Descriptor Systems Based on Multi-Models Concept

This paper addresses the robust fault detection and estimation problem of nonlinear descriptor system with unknown inputs observers. The considered nonlinear descriptor system is transformed into an equivalent multi-models form by using the Takagi-Sugeno (T-S) approach. Two cases are considered: the first one deals with the multi-models with measurable decision variables and the second one assumes that these decision variables are unmeasurable. Then, a residual generator based on an unknown observer is designed for fault detection and estimation. Stability analysis and gain matrices determination are performed by resolving a set of Linear Matrices Inequalities (LMIs) for both cases. The performances of the proposed fault detection and estimation method is successfully applied to an electrical circuit.