On Local Structural Stability of Differential 1-Forms and Nonlinear Hypersurface Systems on a Manifold with Boundary

In this paper we consider smooth di erential 1-forms and smooth nonlinear control-a ne systems with (n 1)-inputs evolving on an ndimensional manifold with boundary. These systems are called hypersurface systems under the additional assumption that the drift vector eld and control vector elds span the tangent space to the manifold. We locally classify all structurally stable di erential 1-forms on a manifold with boundary. We give complete local classi cation of structurally stable hypersurface systems on a manifold with boundary under static state feedback de ned by di eomorphisms, which preserve the manifold together with its boundary.