无界算子扰动下随机发展系统的稳定性

Stochastic Evolution System under Perturbations of Unbounded Operators

柱布朗运动是布朗运动在无穷维空间上的一种重要实现。考虑一类实可分Hilbert空间上被无界算子扰动的关于柱布朗运动的随机发展系统的稳定性问题。运用线性算子半群理论给出了分别使得此系统稳定、使其L2 —连续发展解指数稳定及使其发展解指数稳定的状态反馈控制律 。

We consider stability of stochastic evolution system about cylindrical Brownian motion B(t), t≥0 on real decomposable Hilbert space:dx=(A+P) d t+Qu d t+G(x) d B(t),x(0)=x 0,t≥0. In this system, the infinitesimal generator A is perturbed by a family of unbounded operators p or p . Using semigroup theory of linear operators, it is shown that, under some certain assumptions, the state feedback control laws can be found which make this system stable uniformly with respect to the set p and its evolution solution or L 2 continuous evolution solution exponentially stable in the mean square sense uniformly with respect to the set p .