Joint interval state and actuator fault estimation for linear discrete-time delayed systems

This paper proposes an interval fault estimation method for discrete-time linear systems with known constant time-delay, affected by unknown actuator faults. The disturbances and measurement noise are supposed to be unknown but bounded. By considering the fault vector as an auxiliary state, the original system is converted to an augmented descriptor system. Based on this approach, an interval observer design providing more degrees of design freedom is proposed to estimate simultaneously system states and actuator faults. In order to enhance the estimation accuracy, an H∞ formalism is used to reduce the effects of disturbances and noises. Then, via a linear matrix inequalities (LMI) technique, sufficient conditions for the existence of the proposed observer are obtained. Numerical simulations of a two-stage chemical reactor with delayed streams are given to illustrate the efficiency of the proposed method.