Observer-Based $\mathcal{H}_{\infty }$ Fault-Tolerant Control for Linear Systems With Sensor and Actuator Faults

Abstract

In this paper, the design problem of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> observer-based fault-tolerant control is considered for three faulty cases: sensor only, actuator only, and both sensor and actuator faults. The observers are designed for estimating both states and faults. To reduce the fault effects on the system, virtual observers are first introduced. Based on the virtual observer, real observers are established because the virtual observers include unmeasurable information of the system. By using the estimated information from the observers, observer-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> fault-tolerant controllers are designed. A numerical example is provided to demonstrate the effectiveness of the proposed method.