@inbook{da8eb88572594c75bdd3fa4e74f254f2,
title = "Sliding Modes and Lyapunov Functions for Differential Inclusions by Linear Programming",
abstract = "Recently the concept of essential neighbours of simplices was introduced for switched systems and differential inclusions with triangulated state spaces. It was used to design an algorithm that was able to compute Lyapunov functions for such systems with a strongly asymptotically stable equilibrium, of which the Filippov regularization does not have a strongly asymptotically stable equilibrium. Here we advance this algorithm further and show that the methodology can additionally be used to localize the sliding modes is differential inclusions. Using this localization we can remove constraints from a linear programming problem, whose feasible solutions parameterize Lyapunov functions for the system. We demonstrate the efficacy of our new approach for three systems from the literature.",
keywords = "Differential inclusions, Lyapunov function, Numerical algorithm, Sliding modes, Switched systems",
author = "Sigurdur Hafstein",
note = "Funding Information: This research was supported by the Icelandic Research Fund (Rann{\'i}s) grant number 163074-052, Complete Lyapunov functions: Efficient numerical computation. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 17th International Conference on Informatics in Control, Automation and Robotics, ICINCO 2020 ; Conference date: 07-07-2020 Through 09-07-2020",
year = "2022",
month = jan,
day = "1",
doi = "10.1007/978-3-030-92442-3\_29",
language = "English",
isbn = "9783030924416",
series = "Lecture Notes in Electrical Engineering",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "584--606",
editor = "Oleg Gusikhin and Kurosh Madani and Janan Zaytoon",
booktitle = "Informatics in Control, Automation and Robotics - 17th International Conference, ICINCO 2020, Revised Selected Papers",
address = "Germany",
}