On Local Structural Stability of Differential 1-Forms and Nonlinear Hypersurface Systems on a Manifold with Boundary |
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Authors: | Wojciech Domitrz |
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Affiliation: | (1) Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warszawa, Poland. domitrz@mini.pw.edu.pl, wdomitrz@ise.pw.edu.pl., PL |
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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.
Date received: March 30, 2000. Date revised: October 30, 2000. |
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Keywords: | , Hypersurface systems, Feedback classification, Structural stability, Differential 1-forms, Singularities, |
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