Necessary and sufficient conditions of the subcriticality for linear control systems

A linear control system with continuous coefficients is considered. We obtain a sufficient condition of the subcriticality for such system. The necessary condition of the subcriticality for a linear time-invariant system is obtained. The link between subcritical linear systems and completely controllable linear systems is studied. It is proved that a linear system is completely controllable on closed interval if the system is subcritical at some point in the interior of this interval. It is proved that a completely controllable linear time-invariant system with one-dimensional control is subcritical.