Considering a retarded nonlinear system, this note proposes several modifications of the Lyapunov–Razumikhin approach guaranteeing the existence of an upper estimate on convergence rate of the system solutions. The cases of exponential, finite-time and fixed-time (with respect to a ball) convergences are studied. The proposed approach is illustrated by simulation of academic examples.

中文翻译：

---

Lyapunov–Razumikhin方法的收敛速度估计

考虑到滞后非线性系统，本注释提出了对Lyapunov–Razumikhin方法的一些修改，以保证存在对系统解的收敛速度的较高估计。研究了指数，有限时间和固定时间（相对于球）收敛的情况。通过对学术实例的仿真来说明所提出的方法。