本文研究了Duffing-Van der Pol振子在一类时滞反馈控制下零解的稳定性问题以及极限环的振幅和稳定性问题。依平均法和对时滞反馈控制项泰劳展开的截断得到的平均方程表明，零解的稳定性除与原方程中线性项的系数有关外，只与线性反馈有关，与非线性反馈无关。通过调整线性反馈的增益和时滞，可以使不稳定的零解变得稳定。零解发生Hopf 分岔导致的周期解的振幅除与原方程中非线性项的系数有关外，与线性反馈和非线性反馈均有关。通过调整反馈增益和时滞，不仅可以控制极限环的振幅，还可以抑制极限环的产生。此外，根据平均方程还容易发现反馈时滞对系统动力学行为的影响具有周期性。数值仿真的结果验证了理论分析的正确性。

The dynamical behaviour of a Duffing-van der Pol oscillator under a class of linear-plus-nonlinear state feedback control with a time delay is investigated in this paper by means of the method of averaging. The two slow-flow equations on the amplitude and phase of response are siplified by truncating the Taylor expansions of those terms containing time deklay . It is shown that the stability of the trivial solution is only associated with the coefficients of linear terms, including the gains of linear feedback control, in the original system. Therefore the trivial solution can be stabilized by appreciate choice of gains and time delay of linear feedback, which indicates that limit cycles can be eliminated. Different from the case of the trivial solution, the amplitude of nontrivial solutions is also associated with the coefficients of nonlinear terms besides linear terms in the original systems. However, limit cycles may disappear through amplitudes being infinite or zero when control parameters are varied. It is noticeable that the effect of time delay in feedback control on dynamical systems is peridoc. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.