Abstract
This paper develops a new unknown input observer (UIO) design method for a class of discrete-time linear descriptor systems when the observer matching condition is not satisfied. By equivalent transformations, the state and unknown input observations of the descriptor system are changed to the UIO design problem for a general linear dynamic system firstly. Then based on some further discussion on the concept of the system left invertibility, a new auxiliary output vector is constructed which allows us to remove the unknown inputs from the dynamic equation, and thereby a Luenberger-type observer can be constructed. One of the advantages of the present method is that it can work only under the single strongly detectable condition. Finally, a simulation example is given to verify the effectiveness and show the superiorities of our methods.