Semi-global stabilization of linear time-delay systems with control energy constraint

This note is concerned with the problem of semi-globally stabilizing a linear system with an input delay and a constraint on the energy of its input. Under the condition of null controllability with vanishing energy, the parametric Lyapunov equation based L 2 low gain feedback is adopted to solve the problem. The proposed approach is applied to the linearized model of the relative motion in the orbit plane of a spacecraft with respect to another spacecraft in a circular orbit around the Earth to validate its effectiveness.