On properties of pointwise degenerate linear autonomous control systems. I

Consideration was given to the pointwise degenerate control systems and the problem of full controllability of the linear autonomous system. A procedure was proposed to close this system by a delay controller such that the closed-loop system becomes pointwise degenerate along the directions corresponding to the phase variables of the initial system. At that, the roots of the characteristic polynomial of the closed-loop system can be taken negative, that is, the closed-loop system turns out to be asymptotically stable.