Abstract: The problem on stability of second order differential equations with both impulse and delay is investigated.By employing appropriate Lyapunov functional,stability theory and the method controled by impulses,it is proved that unstable second order differential equations can be stabilized by imposition of impulsive controls.The results extend and improve the recently known results.An example is given to show the effectiveness and less conservatism of the proposed criteria.

Key words: stability, second order differential equations, delay, impulse, Lyapunov functional

摘要： 研究了带脉冲和时滞的二阶微分方程的稳定性问题。通过构造合适的Lyapunov函数,利用稳定性理论和脉冲控制方法,证明了对于不稳定的时滞二阶微分方程,可以通过加强一定的脉冲控制使其稳定。获得的结果改进和推广了前人的工作,提供的例子表明了获得结果的有效性。

关键词: 稳定性, 二阶微分方程, 时滞, 脉冲, Lyapunov函数