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

This 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.