Abstract: The control of approaching phase of the space rendezvous and berthing often uses the parallel approaching method based on the signal of the line of sight (LOS) position. The nonlinear sliding modal in the longitudinal control is improved by adding the coupled item and the damping item including the LOS angle. Its existence and stability are proved for the relative equations. The coupled multivariable nonlinear sliding modal of the LOS guidance is presented. The existence and stability are proved for the coordinated control.

Key words: rendezvous and berthing, parallel approaching method, nonlinear slide modal