Truncated predictor feedback for periodic linear systems with input delays with applications to the elliptical spacecraft rendezvous

Abstract

This paper considers stabilization of periodic linear systems with time-varying input delays. The truncated predictor feedback (TPF) approaches established earlier for time-invariant systems are generalized to the time-varying setting. By carefully investigating the solutions and properties to a class of parametric Lyapunov differential equations, it is proved the TPF controllers can indeed stabilize the concerned time-varying linear time-delay systems for 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 on the elliptical spacecraft rendezvous problem and numerical simulations validate the effectiveness of the established approaches.