@article{e880c78da1f34185b81c8103e40312e3,
title = "Stability analysis of switched systems using variational principles: An introduction",
abstract = "Many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode. Switched systems provide a suitable mathematical model for such processes, and their stability analysis is important for both theoretical and practical reasons. We review a specific approach for stability analysis based on using variational principles to characterize the {"}most unstable{"} solution of the switched system. We also discuss a link between the variational approach and the stability analysis of switched systems using Lie-algebraic considerations. Both approaches require the use of sophisticated tools from many different fields of applied mathematics. The purpose of this paper is to provide an accessible and self-contained review of these topics, emphasizing the intuitive and geometric underlying ideas.",
keywords = "Absolute stability, Bang-bang control, Bilinear systems, Differential inclusions, Dynamic programming, Geometric control theory, Global asymptotic stability, Hamilton-Jacobi-Bellman equation, Hybrid systems, Lie algebra, Lie bracket, Maximum principle, Nilpotent control systems, Reachability with nice controls, Stability under arbitrary switching, Switched controllers",
author = "Michael Margaliot",
note = "Funding Information: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Editor Manfred Morari. This research was supported in part by the ISF under Grant number 199/03. ",
year = "2006",
month = dec,
doi = "10.1016/j.automatica.2006.06.020",
language = "אנגלית",
volume = "42",
pages = "2059--2077",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier Ltd.",
number = "12",
}