In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not assumed to be uncorrelated, only bounds on the mean and the covariance matrices are supposed to be known. This allows to consider nonlinear stochastic systems approximations and the effect of nonlinear filters on the disturbance. The correlation bound concept is introduced and employed to determine probabilistic reachable sets and probabilistic invariant sets. Constructive methods for their computation, based on convex optimization, are given.

中文翻译：

---

具有相关扰动的线性系统的概率可达和不变集

在本文中，提出了一种用于确定和计算由随机扰动激发的线性离散时间系统的概率可达和不变集的构造方法。不假定干扰信号的样本是不相关的，只假定已知平均值和协方差矩阵的界限。这允许考虑非线性随机系统近似和非线性滤波器对干扰的影响。相关界概念被引入并用于确定概率可达集和概率不变集。给出了基于凸优化的计算方法。