Minimax Observers for Linear DAEs

In this note we construct minimax observers for linear stationary DAEs 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 $\mathrm{\ell }$-impulse observable ($\mathrm{\ell }$-detectable) . Remarkably, the regularity of the DAE is not required.