Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm

•Controller design is based on sampled-data equivalent models.•Larger sampling periods can be allowed in the stable operation of closed-loop system.•A discrete-time predictor is constructed to compensate input delays of arbitrary length.•Approximate controllers provide better control performance than emulation control schemes.•Lower order approximate predicted states need only to be computed. In this paper, the problem of global sampled-data stabilization is investigated for high-order nonlinear systems with arbitrarily long input delays. Based on the Lie algebra technique in nonlinear control theory, a discrete-time predictor-based multi-rate sampled-data state feedback control law with a series expansion form is proposed to ensure that the resulting system is globally asymptotically stable under some conditions. Compared with the existing methods, the proposed control algorithm just needs to know the approximate prediction of state variables, and the faster decrease of Lyapunov function may be provided for each subsystem. Performance of approximate versions of the proposed controller is given by theoretical analyses. It is showed that the approximate controllers achieve practical stability of the sampled-data closed-loop system. Finally, the obtained stabilization results are applied to a trajectory tracking problem for a high-order planar system.