Observer Design for Simultaneous State and Fault Estimation for a Class of Implicit Linear Models

A new observer design in explicit structure for a class of implicit linear models (ILMs) in presence of actuator and sensor faults is given in this paper. First, the study is based on the second equivalent form of an implicit model [1] where the differential equations are completely separated of the algebraic equations. Next, the observer is designed to estimate simultaneously the unknown states, the actuator faults and the sensor faults. The condition of exponential stability is given in term of linear matrix inequality (LMI) by using the Lyapunov theory. Finally, an application to an ILM of a heat exchanger process is presented to illustrate the performance of the proposed method.