Partial impulse observability of linear descriptor systems

TL;DR

This paper revises the understanding of partial impulse observability in linear descriptor systems by correcting a previous algebraic criterion and introducing new rank and Wong sequence characterizations.

Contribution

It provides a corrected algebraic criterion and new characterizations for partial impulse observability in linear descriptor systems.

Findings

Corrected the algebraic criterion for partial impulse observability.

Introduced a new rank condition involving system matrices.

Presented an alternative characterization using Wong sequences.

Abstract

A research paper in this journal vol. 61, no. 3, pp. 427-434, 2012, by M. Darouach, provides a functional observer design for linear descriptor systems under the partial impulse observability condition. The observer design is correct, but there was a flaw in the algebraic criterion characterizing partial impulse observability. In the present paper, we derive a novel characterization of partial impulse observability in terms of a simple rank condition involving the system coefficient matrices and an alternative characterization in terms of the Wong sequences.