<p>In the field of rough set research, attribute reduction in information systems remains a core issue. Especially in dynamic information systems, the efficient updating of attribute reduction is crucial. This paper focuses on the local pessimistic multi-granulation covering rough set model. Matrix-based methods are employed to investigate attribute reduction. In addition, incremental techniques are applied to explore dynamic updating reduction, which significantly accelerates the attribute reduction process. First, we provide definitions and relevant properties of the lower and upper approximation sets for the proposed model in this paper. Second, a matrix-based approach is introduced to compute the lower approximation sets in covering decision information system (CDIS). Subsequently, by integrating matrix-based methods with the discernibility matrix, the attribute reduction process and corresponding algorithm are presented. And, in the process of attribute reduction, two conclusions are drawn: the relationship between the matrices for computing approximation sets and the discernibility matrix for reduction, and the relationship between the characteristic function of positive region and the Boolean matrix of discernibility matrix. Finally, for dynamic CDISs with changing attributes, we investigate updating reduction by combining matrix methods with incremental strategies, and provide two dynamic attribute reduction algorithms. The experimental results on ten UCI datasets demonstrate that the algorithms and methods proposed in this paper are effective and feasible.</p>