STABILITY ANALYSIS FOR DELAY DIFFERENTIAL EQUATIONS WITH MULTIDELAYS AND NUMERICAL EXAMPLES

Abstract. In this paper we are concerned with the asymptotic stability of the delay differential equation x ′ n∑ (t) =A0x(t)+ Akx(tτk), k=1 where A0,Ak ∈ Cd×d are constant complex matrices, and x(tτk) = (x1(t − τk1),x2(t − τk2),...,xd(t − τkd)) T,τkl> 0standforn × d constant delays (k =1,...,n,l =1,...,d). We obtain two criteria for stability through the evaluation of a harmonic function on the boundary of a certain region. We also get similar results for the neutral delay differential equation x ′ m∑ n∑ (t) =Lx(t)+ Mix(t − τi)+ Njx ′ (t − τ ′ j), i=1 j=1 where L, Mi, and Nj ∈ Cd×d are constant complex matrices and τi,τ ′ j> 0 stands for constant delays (i =1,...,m, j =1,...,n). Numerical examples on various circumstances are shown to check our results which are more general than those already reported. 1