Stabilization of nonlinear systems by derivative control

The nonlinear multivariable totally controllable system is considered. The admissible control is the feedback control by derivative. The aim is to define the feedback vector, which provides total exponential stability for closed loop system. The solution is performed by canonical nonlinear similarity transformation, providing Frobenious form for the object matrix of the transformed system. The sufficient condition of existence of such a feedback vector and its explicit form are defined.