Abstract
Lie algebras are receiving increasing attention in the field of systems theory, because they can be used to represent many classes of physically motivated nonlinear systems and also switched systems. It turns out that some of the concepts studied in this book, such as the Darboux polynomials and the Poincaré–Dulac normal form, are particularly interesting when referred to Lie algebras. An important application of the concepts of this book is the computation of nonlinear superposition formulas for finite dimensional Lie algebras; such computations are based on first integrals. The last sections of this chapter, based on the exponential notation, deal with the Wei–Norman equations and their use, both for the computation of the solution of systems described by Lie algebras and for the derivation of commutation rules.
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Menini, L., Tornambè, A. (2011). Lie Algebras. In: Symmetries and Semi-invariants in the Analysis of Nonlinear Systems. Springer, London. https://doi.org/10.1007/978-0-85729-612-2_6
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DOI: https://doi.org/10.1007/978-0-85729-612-2_6
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