Robust state observer design guaranteeing D-stability

Abstract

In this paper we consider the observer design problem for uncertain linear systems with D-stability constraints. This problem aims at designing the gain-scheduled slate observers such that, for all admissible parameter uncertainties in slate and output equations, the poles of the observation matrix are placed inside the prespecified disk, and therefore the observation process will possess the desired robustness and transient property. An effective, unified, parametric matrix inequality approach is developed to solve the addressed problem for both continuous- and discrete-time cases. Conditions for the existence of desired robust observers are derived, and the analytical expression of these observers is then characterized. The main results are also extended to the case when an H_∞ performance requirement is added. Furthermore, the application of these results to the design of robust fault detection filters is presented. Finally, the validity and applicability of the present approach are illustrated by two numerical examples.

Notes

E-mail: [email protected]. Zidong Wang is on leave from the Department of Automatic Control. Nanjing University of Science and Technology. Nanjing 210094, P. R. China.