High-order fully actuated system models for discrete-time strict-feedback systems with increasing dimensions

This work aims to propose a high-order fully actuated system (FAS) model for discrete-time strict-feedback systems with nonuniform dimensions. In most of existing works, the authors only consider strict-feedback systems with uniform dimension, i.e. all subsystems have the same dimension. In contrast, we assume that the subsystems may have different or nonidentical dimensions. In particular, the dimensions are assumed to be increasing. Both step-forward and step-backward FAS models for discrete-time strict-feedback systems with nonuniform dimensions are given, based on which the exponentially stabilised controllers can be directly obtained. We consider not only first-order strict-feedback systems but also second-order case.