非线性时滞系统的随机稳定化

Stochastic stabilization of nonlinear systems with time delay

本文讨论非线性时滞系统的随机稳定化问题。对于给定的非线性时滞系统,通过引入一个随机噪音项,可得到一个新的非线性随机时滞系统。在给定条件下,对于任意给定初值,可保证该非线性随机时滞系统具有唯一整体解,且该精确解以一般衰减速度几乎处处稳定。

Stochastic stabilization for nonlinear systems with time delay is discussed in this paper. For a given nonlinear system with time delay,introducing a stochastic noise can afford a new nonlinear stochastic differential system with time delay. Moreover,the new system has a unique global solution for any initial value under certain conditions,and the exact solution shows almost sure stability with a general decay rate.