基于一类非线性时滞系统解的二次可积性研究

利用V函数、Lyapunov泛函、Beuman-Bihari不等式等方法探讨了一类二阶非线性时滞系统的相关性态,诸如振动性、稳定性、周期性及二次可积性等,得到了该类系统相应的充分性存在性条件的有关定量化结论.最后,将所得结论应用到电力系统中三相非同期合闸的过电压模型中,结果表明所得结论与实际背景的物理意义相吻合,同时结论的所有条件较容易验证,因此该结论具有一定的理论意义并便于在实际中应用.

Quadratic integrability of solutions based on a class of delayed systems

Some properties such as oscillation,stability,existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function,the Lyapunov functional or the Beuman-Bihari inequality,and some sufficient conditions based on those properties are given.Finally,the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems,the results in accord with the background physical meaning are obtained.And all the conditions of the conclusions are easy to validate,so the conclusions have definite theoretical meaning and are easy to apply in practice.