Routh-Hurwitz Stability Analyzer

MATLAB App for symbolic and numeric stability analysis using Routh-Hurwitz criterion.

Routh-Hurwitz Stability Analyzer (MATLAB Toolbox)

This MATLAB toolbox provides a graphical user interface (GUI) for analyzing the stability of linear time-invariant (LTI) systems using the classical Routh-Hurwitz criterion.

It supports both **symbolic** and **numeric** polynomial input, generates the corresponding Routh-Hurwitz table, evaluates sign changes, and determines system stability. In numeric mode, it also plots the roots of the characteristic polynomial on the complex plane.

Designed with researchers, students, and educators in mind, this tool aims to reduce human error, improve conceptual understanding, and simplify documentation in control system analysis.

Features

- Symbolic and numeric input modes

- Polynomial auto-generation from degree or coefficients

- Routh-Hurwitz table generation with sign change detection

- Root plotting for numeric cases

- Downloadable results and plots

- Built-in help section for new users

- Developed in MATLAB R2025a using App Designer

Installation

1. Download the `.mltbx` file

2. Open MATLAB

3. Either:

- Double-click the file

- OR run: `matlab.addons.install('RouthStabilityAnalyzer.mltbx')`

4. Launch the app from the **APPS** tab in MATLAB

Intended Users

- Control theory students and educators

- Researchers working on stability analysis

- Engineers designing or testing control systems

Notes

- Works only for algebraic polynomials (not transcendental/logarithmic ones)

- All functionality is self-contained in the toolbox

- For transparency, the backend `routhAnalyzer.m` is also included

Author

Harshit Pranjal

Department of Mathematics, Birla Institute of Technology, Mesra

[e-mail]

Related Research Paper (Coming Soon)

This toolbox is accompanied by a research paper explaining the mathematical basis, design logic, and use cases. It will be submitted to a peer-reviewed journal and linked here when published.