Control theory with singular state-space constraints

A new concept of partially defined system on a singular set is introduced. The setting is based on sheaf theory, and on a concept of locally integrable vector field on a differentiable space, introduced by K.Spallek. Short introductions to both areas are provided. The results consist of accessibility and observability criteria. They extend classical theorems as well as local observability criterion given recently by Bartosiewicz. Also an overview of integrability conditions for Lie-algebra sheaves is presented.