Geometrical Structures of Certain Class of Statistical Manifolds

The geometrical structures of the certain class of statistical manifolds are investigated. The geometrical metrics of such statistical manifolds are obtained, which includes the original geometrical metrics of S. Amari.     

Geometric Structures of Stable Time-Variant State Feedback Systems

A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.