Integrated design of fault estimation and fault-tolerant control of the linear system

The one step LMI based integrated fault estimation and fault-tolerant control problem is considered for the system with actuator and sensor faults. Based on multiple coordinate transformations, a new fault reconstruction observer is designed, which can simultaneously estimate the system state and the faults, even for systems with time-varying and large amplitude faults. For the case where there is no disturbance, the error dynamic can be asymptotically stable. The observer-based fault-tolerant controller is designed. By considering freedom parameter matrices, the one step LMI based integrated algorithm is achieved, which can calculate the observer and the controller parameters simultaneously. The proposed integrated algorithm can prevent the observer estimation error from injecting into the control system. The root-mean-square (RMS) performance is introduced, which can attenuate the effect of disturbances and remove the zero initial condition. Finally, simulations are provided to demonstrate the proposed method.