In this paper, the problems of finite-frequency fault estimation (FE) and fault tolerant controller design are investigated for a class of systems subjected to both sensor and actuator faults. To begin with, by introducing an expanded state vector, the original system is transformed into a descriptor system, and then an unknown input proportional-integral observer (PI) is developed to provide state and FE, which avoids the overdesign problems occurring in the entire frequency domain. After this, based on reconstructed information, an observer-based fault-tolerant controller is designed to stabilize the closed-loop system even if it suffers from faults and disturbances. In addition, the sufficient conditions of the existence of the PI and fault tolerant controller are derived by linear matrix inequality (LMI) tools. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed techniques.
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