State and fault estimation of singular delayed LPV systems via proportional-integral observer

In this paper, a singular LPV system with multiple time varying delays in state is considered. The system is subject to input disturbances and actuator faults. First, the considered system is transformed to polytopic representation and then a polytopic proportional-integral unknown input observer (PI-UIO) is designed for it. This observer can estimate both the system states and the actuator faults in the system. The conditions for disturbance decoupling and also the existence and convergence of the PI-UIO are combined and then obtained in a set of LMIs in the polytope vertices. Actuator fault diagnosis is achieved via the fault estimates provided by the observer. The applicability of the proposed scheme is illustrated via a numerical example.