Impulse Elimination and Fault-Tolerant Preview Controller Design for a Class of Descriptor Systems

In this paper, a fault-tolerant preview controller is designed for a class of impulse controllable continuous time descriptor systems with sensor faults. Firstly, the impulse is eliminated by introducing state prefeedback; then an algebraic equation and a normal control system are obtained by restricted equivalent transformation for the descriptor system after impulse elimination. Next, the model following problem in fault-tolerant control is transformed into the optimal regulation problem of the augmented system which is constructed by a general method. And the final augmented system and its corresponding performance index function are obtained by state feedback for the augmented system constructed above. The controller with preview effect for the final augmented system is attained based on the existing conclusions of optimal preview control; then, the fault-tolerant preview controller for the original system is obtained through integral and backstepping. The relationships between the stabilisability and detectability of the final augmented system and the corresponding characteristics of the original descriptor system are also strictly discussed. The effectiveness of the proposed method is verified by numerical simulation.