In this paper, the H∞, control problem based on a state observer for descriptor systems is investigated. The motivation of this paper is two-fold.
One is to extend the corresponding H∞. results for linear time invariant systems to the case for descriptor systems. The other is to obtain more explicit results
compared to those in the existing literature. From the results obtained here, one can ... [Show full abstract] figure out some special features for
singular systems, which are different from normal linear systems. Also the approach adopted here is pure algebraic, which
is easy to understand. As to the results, a necessary and sufficient condition for the solvability of the H∞. control problem based observer design is obtained in terms of a Generalized Algebraic Riccati Inequality (GARI). Moreover,
the desired controller is also explicitly constructed in this case.