Band criteria and recursive tests of complete controllability and observability of linear algebraic-differentiable systems

New criteria are introduced of complex controllability and observability of controllable linear stationary algebraic-differentiable systems with many inputs and outputs, which reduce to the calculation of the rank of special band matrices. Recursive tests are set up, which permit reducing computational expenses in the verification for the fulfillment of the conditions of complete controllability and observability of algebraic-differentiable systems of a large dimension.