On Path-Complete Lyapunov Functions: Geometry and Comparison

Matthew Philippe, Nikolaos Athanasopoulos, David Angeli, Raphael M. Jungers

Research output: Contribution to journalArticle

3 Citations (Scopus)
199 Downloads (Pure)

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.
Original languageEnglish
JournalIEEE Transactions on Automatic Control
Early online date06 Aug 2018
DOIs
Publication statusEarly online date - 06 Aug 2018

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