This paper investigates the characteristics of the variable-augmented-based free-weighting matrices and studies their application to the stability analysis of the systems with time-varying delay. First, the higher-order terms of time-varying delay are avoided in estimating the derivative of the Lyapunov–Krasovskii functionals by introducing the variable-augmented-based free-weighting matrices such that an improved stability condition is obtained. Then, a general form of the variable-augmented-based free-weighting matrices is given and their common characteristics and additional functions are analysed. As a result, a basic criterion to remove the unnecessary free-weighting matrices is given to derive some results with less free-weighting matrices. Finally, a numerical example is given to show the effectiveness and merits of the presented method and analysis.
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He et al. (2022) studied this question.