Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation

In this note, the problem of observer design for linear descriptor systems with faults and unknown inputs is considered. First, it is considered that the fault vector function f is s~ times piecewise continuously differentiable. If the s~th time derivative of f is null, then s~ integral actions are included into a Luenberger observer, which is designed such that it estimates simultaneously the state, the fault, and its finite derivatives face to unknown inputs. Second, when the fault is not time piecewise continuously differentiable but bounded (like actuator noise) or s~th time derivative of fault is not null but bounded too, a high gain observer is derived to attenuate the fault impact in estimation errors. The considered faults may be unbounded, may not be determinist, and faults and unknown inputs may affect the state dynamic and plant outputs. Sufficient conditions for the existence of such observer are given. Results are illustrated with a differential algebraic power system.