【摘要】 本文将二维系统的可达性格拉姆矩阵Ｋ，可观测性格拉姆矩阵Ｗ和噪声格拉姆矩阵ＷＮ推广到多维数字系统，导出了Ｗ与ＷＮ的显式关系式．文中证明，Ｋ和ＷＮ满足一对修正的李亚普诺夫矩阵方程，对于分母可分的系统，Ｋ和ＷＮ为分块对角阵，且可以通过求解李亚普诺夫矩阵方程组而得．更多还原

【Abstract】 In this paper, the reachability Gramian K, observability Gramian W and noise Gramian WN of2-D systems are extended to multidimensional (n-D) multi-input multi-output (MIMO) digital systems. An exPlicit relationship betWeen W and WN is derived. It is shown that: (1) for general n-D systems, the Gramians Kand WN satisfy a pair of modified discrete-time Lyapunov matrix equations (DTLME); (2) for the causal recursive separable denominator (CRSD) n-D systems,both K and WN are block-diagonal matrices, and they can becomputed by solving n pairs of DTLME.更多还原