Robust stability analysis for uncertain systems with time‐varying delay via variable augmentation approach

Abstract

AbstractThis paper investigates the problem of robust stability analysis for systems with time‐delays and time‐varying structured uncertainties. The variable augmentation approach and the free‐matrix‐based inequality are employed to retain the linear property of the estimation of the derivative of the Lyapunov–Krasovskii functionals. Moreover, with the use of the variable augmentation approach related to the time‐varying structured uncertainties, the time‐varying S‐Procedure combined with the time‐varying delay and its derivative is employed. As a result, less‐conservative robust stability conditions are derived. In addition, the merits of the augmentation of the time‐varying structured uncertainties over the traditional methods are theoretically demonstrated. Finally, two numerical examples are given to verify the benefits of the proposed methods.