Note on asymptotic stability of a class of neutral differential equations

In this work, a new sufficient condition for asymptotic stability of the neutral differential equation of the form ddt[x(t)+px(t−τ)]=−ax(t)+btanhx(t−σ) is established. The condition expressed in terms of a linear matrix inequality (LMI) and dependent on both the delays ττ and σσ is less restricted than that given by J.H. Park [Delay-dependent criterion for asymptotic stability of a class of neutral equations, Applied Mathematics Letters 17 (2004) 1203–1206].