Static anti-windup compensator design for nonlinear time-delay systems subjected to input saturation

In this paper, a novel technique for synthesizing static anti-windup compensator (AWC) is explored for dynamic nonlinear plants with state interval time-delays, exogenous input disturbance, and input saturation nonlinearity, by means of reformulated Lipschitz continuity property. A delay-range-dependent approach, based on Wirtinger-based inequality, is employed to derive a condition for finding the static AWC gain. By using the Lyapunov–Krasovskii functional, reformulated Lipschitz continuity property, Wirtinger-based inequality, sector conditions, bounds on delay, range of time-varying delay, and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}_2$$\end{document} gain reduction, several conditions are derived to guarantee the global and local stabilization of the overall closed-loop system. Further, when the lower time-delay bound is zero, the delay-dependent stabilization condition is derived for saturated nonlinear time-delay systems as a particular scenario of the suggested static AWC design approach. Furthermore, a static AWC design strategy is also provided when a delay-derivative bound is not known. An application to the nonlinear dynamical system is employed to demonstrate the usefulness of the proposed methodologies. A comparative numerical analysis with the existing literature is provided to show the superiority of the proposed AWC results.