Analysis Of Asymptotic Stability Of Generalized Neutral Delay Differential Systems And Numerical Examples

In many realistic models, we should know some past states of the system, thus it converts tothe study of delay differential equation. delay differential equations are often used in life sciences,control theory, electric system.Neutral delay differential equations is a important class of delay differential equations. It ismore complex to deal with because the exist of the neutral item. Unlike the asymptotic stabilityof the necessary and sufficient condition of delay differential equations for which all the charac-teristic roots have negative real parts[21], in the situation of neutral system, relationships betweencharacteristic roots and the stability are more complex. In fact, even if all the roots are negative,the system of NDDEs can still be unstable.In this paper, we are concerned with both delay-independent and delay-dependent stabilitycriteria of the generalized neutral delay differential equations(GNDDEs) are constant delays.We derive two stability criteria via the evaluation of a harmonic function in a bounded re-gion, which are delay-dependent and delay-independent criteria. Then we give some numericalexamples. Numerical experiments on various circumstances are shown how to locate the specificregion which can make the system unstable so as to exclude it from the whole complex-plane.