On full controllability criteria of a descriptor system. The polynomial solution of a control problem with checkpoints

We derive full controllability criteria for a stationary dynamical system described by an algebro‐differential relation with rectangular matrix coefficient. The derivation is done by multistage splitting of the spaces into subspaces in special and general cases. We construct a polynomial control and state of the descriptor system in case the system trajectory passes an arbitrary finite amount of checkpoints without projectors.