On Necessary and Sufficient Conditions to Design Luenberger Observer for Descriptor Systems With Unknown Inputs

ABSTRACT Linear time‐invariant descriptor systems with unknown inputs, not necessarily regular, are studied. The existence conditions for a Luenberger observer for this system are addressed in terms of the system coefficient matrices. Novel necessary and sufficient conditions for the existence of a Luenberger observer have been derived. The proposed rank criteria are milder than those existing in the previous literature. Orthogonal transformations are used to ensure numerical stability. Using the proposed conditions, techniques to design two different reduced‐order Luenberger observers are proposed. Numerical and physical examples illustrate the application.