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

Abstract.

In this paper we consider smooth differential 1-forms and smooth nonlinear control-affine systems with (n−1)-inputs evolving on an n-dimensional manifold with boundary. These systems are called hypersurface systems under the additional assumption that the drift vector field and control vector fields span the tangent space to the manifold. We locally classify all structurally stable differential 1-forms on a manifold with boundary. We give complete local classification of structurally stable hypersurface systems on a manifold with boundary under static state feedback defined by diffeomorphisms, which preserve the manifold together with its boundary.