Stability analysis of some neutral delay-differential equations with a frequency-domain approach (Q2099189)

This paper aims to contribute by introducing an analytical technique based on feedback systems, in order to help to understand the dynamical behavior of neutral delay differential equations (NDDEs). Two general schemes of NDDEs are considered, one of first differential order and another of second order. They represent non-delayed systems with delayed, nonlinear feedback control. The equations are assumed to contain a nonlinear term such that it vanishes simultaneously with its first derivatives at the origin. The stability conditions in terms of system parameters are derived using a frequency-domain approach based on feedback systems, namely, the Nyquist stability criterion. These results are compared with those already found using more classical techniques, namely, those investigating directly the roots of the characteristic equation. Two examples are given to illustrate the usefulness of the approach: Chua's circuit with lossless transmission line and mechanical system with delayed force control.