Sampled-Data Control of Nonlinear Systems with Input Delay via Nonsmooth Feedback

This paper studies sampled-data control of a class of nonlinear systems with input delay by memoryless feedback. A sampled-data nonsmooth feedback controller is first developed based on the emulation method and the adding a power integrator (AAPI) technique Lin and Qian [2000], Qian and Lin [2001]. With the aid of Lyapunov-Krasovskii functional theorem, together with the robust control design, we then prove that the proposed memoryless sampled-data controller renders the hybrid closed-loop systems with delay globally asymptotically stable, if the input delay and sampling period are limited. The family of uncertain systems under consideration goes beyond the global Lipschitz or linear growth condition and is genuinely nonlinear in the sense that it contains uncontrollable unstable linearization and is not smoothly stabilizable, even locally. Application of the nonsmooth sampled-data control scheme is illustrated by a simplified under-actuate mechanical system with input delay. Copyright 2022 (c) The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)