We give a classification of minimal homothetical hypersurfaces in an (n+1)-dimensional Euclidean space. In fact, when n ≥ 3, a minimal homothetical hypersurface is a hyperplane, a quadratic cone, a cylinder on a quadratic cone or a cylinder on a helicoid.
In this paper, we investigate the geometric structures of the stable time-varying and the stable static output feedback systems. Firstly, we give a parametrization of stabilizing time-varying output feedback gains subject to certain constraints, that is, the subset of stabilizing time-varying output feedback gains is diffeomorphic to the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices satisfying certain algebraic conditions....
Page 1