抄録
This paper considers the parametric structure of the controllability of linear time-invariant systems. The set of (A, B), controllable linear time-invariant multi-input systems, is divided into several equivalence classes through controllability indices, These equivalence classes are distributed in the parameter space. The elementary algebraic geometry resolves the algebraic relations of the parameters (A, B) with respect to its controllability indices, and its structure in the parameter space.
The set of (A, B) with the same controllability indices is the intersection of the several algebraic open or closed sets depending on its indices. The insensitivity relation between the controllability indices by the, parametric perturbation is defined based on the algebraic set property in the elementary algebraic geometry.
