On Path-Complete Lyapunov Functions: Geometry and Comparison
Abstract
We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question "can we decide algorithmically when a criterion is less conservative than another". Our contribution is twofold. First, we show that a Path-Complete Lyapunov Function, which is a multiple Lyapunov function by nature, can always be expressed as a common Lyapunov function taking the form of a combination of minima and maxima of the elementary functions that compose it. Geometrically, our results provide for each Path-Complete criterion an implied invariant set. Second, we provide a linear programming criterion allowing to compare the conservativeness of two arbitrary given Path-Complete Lyapunov functions.
Cite
@article{arxiv.1712.00381,
title = {On Path-Complete Lyapunov Functions: Geometry and Comparison},
author = {Matthew Philippe and Nikolaos Athanasopoulos and David Angeli and Raphaël M. Jungers},
journal= {arXiv preprint arXiv:1712.00381},
year = {2017}
}
Comments
12 pages, 9 figures