Observer design and a separation principle for linear discrete-time descriptor sysems

Abstract

This paper addresses the design of state observers for linear discrete-time descriptor systems. Assuming that the original descriptor system is completely observable, an equivalent (standard) state-space representation of the system is proposed which preserves the system observability. Then, an LMI based approach is proposed for designing a Luenberger-like observer. In addition, a separation principle is demonstrated considering the estimation error dynamics and the closed-loop representation of the original descriptor system. Then, the observer design is extended to cope with model disturbances in an H1 sense. The eectiveness of the proposed methodology is illustrated by numerical examples.