Simultaneous Sensor and Actuator Faults Diagnosis in Fornasini-Marchesini Second Model Using Design Unknown Input Observer

This paper discusses the detection and diagnosis of sensor and actuator faults with input and output disturbance in two-dimensional linear systems described by the Fornasini-Marchesini second model. It can be rewritten as a new state variable by augmentation of the sensor fault in the output measurement equation with the state variable. The augmented equation can be rewritten as a descriptor system to estimate the state variables of the new system with actuator faults, and then the design of a new unknown input observer is proposed. This allows the errors of the new state variables and actuator faults to be estimated. The asymptotic stability conditions of the dynamic error of the observer are obtained in terms of linear matrix inequalities. A practical example is provided to demonstrate the effectiveness of the proposed method.