This paper is concerned with the problem of designing an observer for linear descriptor systems Ex = Ax + Bu, Y= Cx. At first, an observer is presupposed to have the same structure as Luenberger Observer, and the fundamental equations that the plant and the observer must satify are derived. Based on these equations, it is shown that an observer exists if the system is observable in the sense of Rosenbrock. And the design methods of an identity observer and a minimal-order observer are presented by utilizing the generalized matrix inverse. Secondly, the realizability condition is relaxed by eliminationg the purely static modes of the system, and it is shown that the observer can be realized if the system is observable in the sense of Verghese.
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