Delay-Derivative-Dependent Stability for Neutral Systems with Time-Varying Delay and Nonlinearity

The asymptotical stability for a class of neutral systems with time-varying delay and restricted nonlinearity is investigated. Firstly, during choosing the Lyapunov–Krasovskii functional (LKF), two adjusting scalars α,β∈(0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha ,\beta \in (0,1]$$\end{document} will be introduced and they can effectively reduce the conservatism once the upper bound of delay derivative is very large. Then by utilizing some integral inequalities, the much tighter bound on LKF derivative is presented and some previously ignored information can be fully utilized by employing an extended convex combination technique. Furthermore, two stability criteria are presented in terms of LMIs and they can be easily checked. Finally, some numerical examples with comparing results can illustrate the superiorities of the derived results.