Using the method of invariant ellipsoids for linear robust output stabilization of spacecraft

Consideration was given to the problem of robust output stabilization of the nonlinear system using the method of invariant ellipsoids on assumption that the system satisfies a Lipschitz-like condition and the system output is subjected to bounded external disturbances. It was reduced to a special optimization problem with solution based on the theory of linear matrix inequalities. The proposed approach was illustrated by an example of stabilization of a spacecraft with elastic dynamic elements. The designed control represents a combination of the “accelerate-decelerate” algorithm and a linear feedback obtained using the method of invariant ellipsoids.