Relay control of undamped linear systems using Lyapunov´s second method

A method is presented for the application of Lyapunov´s second method to the synthesis of relay-control systems for plants that have undamped responses. A technique is presented for overcoming the problems associated with the solution of the Lyapunov matrix equation when the plant eigenvalues have zero real part. The method is applied to the attitude control of a flexible space vehicle.