Relative controllability and relative attainability criteria for linear stationary regular differential-algebraic systems

The problems of $H$-relative controllability and $H$-relative attainability, null-controllability, complete controllability and attainability, controllability in the space $\mathbb R^n$ of linear stationary regular differential-algebraic systems are investigated. For the designated problems the rank solvability criteria are proved. All criteria are formulated in terms of parameters of the initial system and base matrixes.