泛函微分系统依照两个测度的稳定性

Stability Properties In Terms Of Two Measures for Functional Differential Systems

运用变分Lyapunov方法,研究了泛函微分系统依照两个测度的稳定性。首先,给出了关于微分系统的一个Razumikhin型比较定理。进一步,得到一个变分比较定理。根据此结果,在未扰动系统为常微分系统的情形下,建立了关于泛函微分系统依照两个测度稳定性的判定定理,推广并改进了已有结果。

By using the variational Lyapunov method, the stability properties in terms of two measures for functional differential systems are investigated. First, a Razumikhin comparison theorem for differential systems is given. Furthermore, a variational comparison theorem is obtained. Applying this result, in the case that the unperturbed systems are ordinary differential systems, criteria on stability in terms of two measures for functional differential systems are established. The existing results are generalized and improved.