Supplementary Material for Sum-of-Squares Stability Verification on Manifolds with Applications in Spacecraft Attitude Control

<p>This repository contains the supplementary MATLAB code for the paper <i>"Sum-of-Squares Stability Verification on Manifolds with Applications in Spacecraft Attitude Control,"</i> accepted for presentation at the European Control Conference (ECC) 2026 (an extended version is available at <a href="https://arxiv.org/abs/2604.13727" target="_blank">arXiv:2604.13727</a>).</p>

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<h3>Requirements and Setup</h3>
<p>Clean dependency management is seamlessly handled through Git Submodules and MATLAB Project settings. The necessary setup components are contained within the <code>external_dependencies</code> and <code>resources</code> folders.</p>

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<h3>Implementation Details</h3>
<ul>
<li><b>Core Implementations:</b> Located in the <code>scripts</code> folder. This directory contains the example scripts used to obtain Lyapunov functions via Sum-of-Squares Optimization. These scripts can also serve as blueprints for solving similar control verification problems.</li>
<li><b>Aerodynamic Toolbox:</b> The <code>+saero</code> directory houses an object-oriented toolbox for computing aerodynamic torque for Very Low Earth Orbit (VLEO) satellites, specifically employed in the first example.</li>
</ul>

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<h3>Running the Examples</h3>
<p>To get started with reproducing the two example problems outlined in the paper, please follow these steps:</p>
<ol>
<li>Consult the <code>README.md</code> file for initial setup and execution guidelines.</li>
<li>Navigate to the <code>scripts</code> folder to execute the primary verification scripts.</li>
</ol>

<p>For more details on the code structure, you can also visit the corresponding <a href="https://github.com/iFR-OFC/SOS-Verify-Manifold-Spacecraft/tree/main" target="_blank">GitHub Repository</a>.</p>