Linearization through state immersion of nonlinear systems admitting Lie symmetries |
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Authors: | Laura Menini [Author Vitae] Antonio Tornambè [Author Vitae] |
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Affiliation: | Dip. di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133 Roma, Italy |
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Abstract: | In this paper, it is shown that if a nonlinear system admits a Lie symmetry that can be transformed into its Poincaré-Dulac normal form by a state diffeomorphism, then, under some technical conditions, such a nonlinear system can be immersed into a linear one. This allows us to compute in closed-form the flow, all algebraic invariant curves (through semi-invariants) of the nonlinear system, and Lyapunov functions to study stability properties. |
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Keywords: | Nonlinear systems Linearization Co-ordinate transformations State immersion Lie symmetries |
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