Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems

@article{Abate2020LyapunovDE,
title={Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems},
author={Matthew Abate and Samuel D. Coogan and E. Feron},
journal={2020 American Control Conference (ACC)},
year={2020},
pages={5322-5327}
}

This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic Lyapunov functions for a related hierarchy of Lyapunov differential equations. This creates an intuitive procedure for checking the stability properties of switched linear systems, and a computationally competitive algorithm is presented for generating high… Expand