The main contribution of this paper is the design of a polytopic unknown inputs proportional integral observer (UIPIO) for linear parameter-varying (LPV) descriptor systems. This observer is used for actuator fault detection and isolation. The proposed method is based on the representation of the LPV descriptor systems in a polytopic form. Its parameters evolve in an hypercube domain. The designed polytopic UIPIO is also able to estimate both the states and the unknown inputs of the LPV descriptor system. Stability conditions of such observer are expressed in terms of linear matrix inequalities. An example illustrates the performances of such polytopic UIPIO.

This paper presents an Adaptive Polytopic Observer (APO) design in order to develop an actuator fault estimation method dedicated to polytopic Linear Parameter Varying (LPV) descriptor systems. This paper extends a fault diagnosis method developed for regular LTI systems to polytopic LPV descriptor systems.Here, time-varying actuator faults are also considered, whereas in many papers, actuator faults are generally assumed to be constant. The design and convergence conditions of this APO are provided. The design is formulated through LMI techniques under equality constraints. The performances of the proposed actuator fault estimation scheme are illustrated using an electrical circuit. By using (31) and substituting (40) into Equation (38), one can obtain ² u 1 .t / D 12 sin.2:5t / u 2 .t / D 5