Delay-dependent criterionfor asymptotic stability of a class of neutral equations

Abstract

In this letter, a sufficient condition for all solutions of a class of neutral equations to approach zero at t --* c~ is presented. The condition, which is expressed in terms of linear matrix inequality, is delay-dependent and can be easily solved by various efficient convex optimization algorithm. ~)

An improved stability criterion for a class of neutral differential equations

“…(2.8). However, the criterion obtained in [4] cannot be applied since the operator D used in [4] is unstable. Indeed, we consider the equation Dx t = 0 with initial condition…”

“…To compare with the stability criterion obtained in [4], we consider the case α = 0. In this case, we have…”

“…Sun et al in [4] have derived a less conservative stability criterion. However, this condition still depends on the stability of the operator D * .…”

“…• First, we introduce a new Lyapunov functional and avoid the use of the stability assumption on the operator D in [4] or D * in [5]. Hence, our criterion will be less restricted than [4,5] (see Example 2).…”

“…Recently, the asymptotic stability of neutral differential equation (1.1) has been discussed in [1,4,5]. Using stability assumption on the operator…”