Sampled‐data control of time‐delay uncertain systems with uncontrollable/unobservable linearization by memoryless feedback

Abstract

Sampled‐data control problems via memoryless state and output feedback are studied, respectively, for a class of strongly nonlinear systems with state and input delays. Under sample and hold, both state and output feedback control schemes are developed by virtue of the emulation method, the adding a power integrator technique, and the recursive design of nonlinear observers. With the aid of Lyapunov–Krasovskii functional theorem, together with the idea of robust control, we prove that the proposed sampled‐data state and output feedback controllers make the hybrid closed‐loop systems with delays and uncertainty globally asymptotically stable, if the input delay and sampling period are limited. The class of time‐delay uncertain systems under consideration goes beyond the Lipschitz or linear growth condition and is genuinely nonlinear in the sense that it contains uncontrollable/unobservable linearization and is not stabilizable, even locally, by any linear or smooth feedback. Applications of the sampled‐data robust control schemes presented in this article are illustrated by examples with simulations.