In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments.

翻译：本文研究了一种适用于可镇定且可检测的随机系统的模型约简技术。该方法基于一对格兰姆矩阵，我们对其适定性进行了分析。随后，利用这些格兰姆矩阵识别了随机系统的主导子空间。我们提出了一种相关的平衡化方案，通过从随机动力学中剔除次要信息来获得降阶系统。研究表明，该降阶模型保留了可镇定性与可检测性等关键特性。此外，基于格兰姆矩阵对乘积的特征值进行了全面的误差分析，这为降阶质量提供了先验判据，并通过数值实验予以验证。