Almost controllability sets for the almost decoupling of nonlinear systems

Amost invariast and almost controllability subspaces were introduced by Willems for linear systems[7],[8],[9]. These structural tools are useful in solving some sort of almost robust control problems such as almost decoupling, almost disturbances rejection etc. We provide in this paper, a nonlinear generalization of these concepts: almost controllability sets for nonlinear control systems, The main result concerns the almost controllability sets for nonlinear control systems which generate decomposable Lie algebras (e.g. nil potent Lie algebras). Using a theorem of Krenet concerning the bilinear approximations of nonlinear systems, this result is generalized to arbitrary smooth nonlinear systems.