This paper investigates the problem of the absolute stability of neutral systems with a time-varying delay and
sector-bounded nonlinearity. By constructing a novel Lyapunov-Krasovskii functional based on the piecewise analysis
method for the time-varying delay systems, less conservative delay-dependent stability criteria are obtained and formulated
in terms of linear matrix inequalities without ignoring any useful terms in the derivative of a Lyapunov-Krasovskii functional
by using the convex combination method. Numerical example shows the effectiveness of the proposed method.