Minimax Observers for Linear DAEs

TL;DR

This paper develops minimax observers for linear differential-algebraic equations (DAEs) with uncertainties, establishing duality principles and conditions for their existence without requiring DAE regularity.

Contribution

It introduces a new duality principle for minimax observers in DAEs and characterizes their existence based on impulse observability and detectability.

Findings

Finite horizon minimax observers exist under impulse observability.

Infinite horizon minimax observers exist under impulse detectability.

Regularity of the DAE is not necessary for observer existence.

Abstract

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 $\ell$-impulse observable ($\ell$-detectable) . Remarkably, the regularity of the DAE is not required.