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arXiv · 1712.00381

On Path-Complete Lyapunov Functions: Geometry and Comparison

Matthew Philippe·Nikolaos Athanasopoulos·David Angeli·Raphaël M. Jungers
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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.

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Matthew Philippe, Nikolaos Athanasopoulos, David Angeli, Raphaël M. Jungers. 2017-12-01. On Path-Complete Lyapunov Functions: Geometry and Comparison. https://arxiv.org/abs/1712.00381

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