Controllability to the origin implies state-feedback stabilizability for discrete-time nonlinear systems
arXiv:1505.05937 · doi:10.1016/j.automatica.2016.09.046
Abstract
The problem of state-feedback stabilizability of discrete-time nonlinear systems has been considered in this note. Two assertions have been proved. First, if the system is -step controllable to the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in steps. Second, if the system is asymptotically controllable to the origin and satisfies the controllability rank condition at the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in finite steps.
This work was supported by the Japan Society for the Promotion of Science under Grant-in-Aid for Scientific Research (C) 23560535. This document is the accepted version of the manuscript published in Automatica. Copyright 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/