Polyhedral Path-Complete Lyapunov Functions

Athanasopoulos, Nikolaos;Jungers, Raphaël
(2019) 2019 IEEE 58th Conference on Decision and Control (CDC) — Location: Nice, France (11.December.2019)

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Path-complete methods utilize a set of positive definite functions and a specially constructed graph in order to evaluate, among others, stability of switching systems. This tool is shown to be general, e.g., path-complete criteria are universal for linear switching systems and quadratic templates. In this work, we extend the approach to polyhedral Lyapunov functions, and introduce a simple parameterization that can be sufficient for stability analysis. Moreover, we indicate ways of obtaining less conservative stability criteria by partial graph extensions, all evaluated by solving Linear Programs (LPs).
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Athanasopoulos, N., & Jungers, R. (2019). Polyhedral Path-Complete Lyapunov Functions. 2019 IEEE 58th Conference on Decision and Control (CDC). Published. 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France. https://doi.org/10.1109/cdc40024.2019.9029905