A Note on Order and Index Reduction for Descriptor Systems

TL;DR

This paper introduces new methods for order reduction of linear time invariant descriptor systems, connecting classical and recent results, and providing elementary constructions of quasi-Weierstrass forms with illustrative examples.

Contribution

It offers novel order reduction techniques and a straightforward approach to construct quasi-Weierstrass forms for descriptor systems, bridging classical and modern results.

Findings

Established a precise connection between classical and new order reduction results.

Provided methods for constructing reduced order descriptor systems.

Illustrated the usefulness of the methods with examples.

Abstract

We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection between classical and new results on this topic, and lead to an elementary construction of quasi-Weierstrass forms for a descriptor system. Examples are given to illustrate the usefulness of our results.