Stabilization of nonlinear systems with nonstabilizable linearization by direct gradient descent control

This work describes, via example, application of the direct gradient descent control to stabilize asymptotically the nonlinear control systems with nonstabilizable linearization. By applying the direct gradient descent control to the nonlinear control system, we get a new system which depends on one parameter. Furthermore, the value of parameter is determined such that a new system become asymptotically stable.