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

This paper is concerned with semi-global stabilization of linear systems with actuator delay and energy constraints. Under the condition of null controllability by vanishing energy, the parametric Lyapunov equation based L2 low gain feedback is adopted to solve the problem. If the delay in the system is exactly known, a delay-dependent controller is designed and if the delay in the system is either time-varying or not exactly known, a delay-independent controller is established. The proposed approach is used in the linearized model of the relative motion in the orbit plane of a spacecraft with respect to another in a circular orbit around the Earth to validate its effectiveness.