What question did this study set out to answer?

The aim is to determine necessary and sufficient conditions for designing Luenberger observers in systems with unknown inputs.

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

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Reveals conditions for designing Luenberger observers in descriptor systems, suggesting improved stability and applicability.

The aim is to determine necessary and sufficient conditions for designing Luenberger observers in systems with unknown inputs.
Examined linear time-invariant descriptor systems with unknown inputs.
Derived novel existence conditions in terms of coefficient matrices.
Developed rank criteria that are milder than previous conditions.
Utilized orthogonal transformations for enhancing numerical stability.
Proposed techniques for designing two different reduced-order Luenberger observers.
Established new criteria for the existence of Luenberger observers in the studied systems.
Demonstrated that the proposed methods lead to more stable observer designs.
Applied the conditions to numerical and physical examples, illustrating effectiveness.

Paitandi et al. (2026) studied this question.

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