Robust state observer design guaranteeing D-stability

In this paper we consider the observer design problem for uncertain linear systems with D-stability constraints. This problem aims at designing the ga in-scheduled state observers such that, for all admissible parameter uncert ainties in state and output equations, the poles of the observation matrix are placed inside the prespecified disk, and therefore the observation proc ess will possess the desired robustness and transient property. An effectiv e, unified, parametric matrix inequality approach is developed to solve the addressed problem for bath continuous- and discrete-time cases. Conditions for the existence of desired robust observers are derived, and the analyti cal expression of these observers is then characterized The main results ar e also extended to the case when an H-infinity performance requirement is a dded. Furthermore, the application of these results to the design of robust fault detection filters is presented. Finally, the validity and applicabil ity of the present approach are illustrated by two numerical examples.