On improved delay-dependent stability criterion of certain neutral differential equations

Abstract In this letter, the problem for an asymptotic stability of the following neutral differential equation: d d t [ x ( t ) + px ( t - τ ) ] = - ax ( t ) + b tanh x ( t - σ ) is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both τ and σ , is derived in terms of linear matrix inequality (LMI). Two numerical examples are included to show the effectiveness of the proposed method.