Remark on the paper of Park

This paper considers certain neutral differential equation with the distributed delayddt[x(t)+c(t)x(t-τ)]+p(t)x(t)+q(t)x(t-σ)+r(t)∫t-δtx(s)ds=0.Without imposing a nonnegative restriction on coefficients of the equation, we establish a delay-dependent asymptotic stability condition for the equation by introducing a new Lyapunov function. The condition presented here is different from that of Park [J.H. Park, LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients, Appl. Math. Comput. 160 (2005) 355–361] in the sense that it is dependent on all delays of the equation. Numerical examples illustrate effectiveness and sharpness of our theoretical result.