# On Checking Null Rank Conditions of Rational Matrices

## TL;DR

This paper explores numerical methods for reliably verifying the null rank condition of rational matrices using MATLAB tools, focusing on descriptor system realizations.

## Contribution

It introduces numerical approaches for checking the rank condition of rational matrices, utilizing MATLAB's Control System Toolbox and DSTOOLS.

## Key findings

- Proposes numerical algorithms for rank checking.
- Demonstrates methods using MATLAB tools.
- Provides reliable verification techniques.

## Abstract

In this paper we discuss possible numerical approaches to reliably check the rank condition rank $G(\lambda) = 0$ for a given rational matrix $G(\lambda)$ in terms of its descriptor system realization. For test purposes we employ functions available in the Control System Toolbox of MATLAB and the Descriptor System Tools (DSTOOLS) collection.