Truncated Predictor Feedback for Periodic Linear Systems With Input Delays With Applications to the Elliptical Spacecraft Rendezvous

This paper considers truncated predictor feedback (TPF) stabilization of periodic linear systems with time-varying input delays with its applications to the elliptical spacecraft rendezvous. By carefully investigating the solutions and properties to a class of parametric Lyapunov differential equations, it is proved that TPF controllers can stabilize the periodic linear time-delay systems with arbitrarily large and bounded delays as long as the characteristic multiplier set of the open-loop system is within the closed unit circle. Both single input delay and multiple input delays are addressed. Moreover, the control matrices of the systems are not necessarily periodic. The developed TPF approach is then applied to the elliptical spacecraft rendezvous problem, and numerical simulations validate the effectiveness of the established approaches.