Minimax Observers for Linear Differential-Algebraic Equations

In this note we construct minimax observers for linear stationary Differential-Algebraic Equations (DAE)s with bounded uncertain inputs, given noisy measurements. We prove a new duality principle and show that a finite (infinite) horizon minimax observer exists if and only if the DAE is ℓ-impulse observable (ℓ-detectable). Remarkably, the regularity of the DAE is not required.