H∞ optimization of Luenberger state observers and its application to fault detection filter design

This paper considers H_∞ optimization of Luenberger state observers. The conventional formulation of H_∞-optimal state observers does not allow the augmentation of dynamic performance weightings in the optimization objective, since it makes the problem a nonconvex optimization problem. We propose an algorithm to locally solve an H_∞ optimization problem of Luenberger state observers by transforming the problem into an H_∞ optimization problem of a static output feedback controller. The proposed approach offers an intuitive and efficient way to explicitly design the estimation error dynamics of the observer in the frequency domain. As an application example, the proposed approach is applied to the tuning of fault detection filters for lateral control of automated passenger vehicles. Numerical simulations are conducted to show the effectiveness of the proposed tuning method