# Stability tests for a class of switched descriptor systems with non-homogenous indices

## TL;DR

This paper develops stability conditions for switched descriptor systems with varying indices, including cases switching between standard and index one or two descriptor systems, supported by illustrative examples.

## Contribution

It introduces new stability criteria for switched descriptor systems with non-homogeneous indices, covering cases previously not well-understood.

## Key findings

- Derived stability conditions for switched descriptor systems with different indices
- Applicable to systems switching between standard and index one or two descriptor systems
- Validated results with illustrative examples

## Abstract

In this paper we derive stability conditions for a switched system where switching occurs between linear descriptor systems of different indices. In particular, our results can be used to analyse the stability of the important case when switching between a standard system and an index one descriptor system, and systems where switching occurs between an index one and and an index two descriptor system. Examples are given to illustrate the use of our results.