Cascade decomposition of nonlinear systems, foliations and ideals of transitive Lie algebras (Q1057221)

In this research announcement the notions of cascade decomposition and parallel decomposition of a nonlinear control system are connected with similar concepts for the associated system's Lie algebra. In particular a nonlinear system admits a cascade decomposition if the Lie algebra of the system has a nontrivial ideal whereas a parallel decomposition corresponds to a direct sum decomposition into two nontrivial ideals of this algebra. Further details are reported by the same author [Décompositions en cascades des systèmes automatiques et feuilletages invariants'', to appear in Bull. Soc. Math. France].