Optimal transients damping under constraints for Euclidean norm of the control vector

In the paper an application of V.I. Zubov´s optimal transient damping method for control-affine objects which dynamics is described in the state space by nonlinear ordinary differential equations is considered. The control problem is solved under the constraint for maximal value of the Euclidean norm of control vector. Lyapunov function of the control object is used as the damped scalar function. The derivative of Lyapunov function is obtained in the form of the matrix polynomial using the matrix power series method. An example of the application of the proposed method for the permanent magnet synchronous motor speed control is shown.