Reachability, Observability and Noise Gramians of Multidimensional MIMO Digital Systems

肖承山; 冯振明

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Reachability, Observability and Noise Gramians of Multidimensional MIMO Digital Systems

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- Reachability, Observability and Noise Gramians of Multidimensional MIMO Digital Systems
- Acta Electronica Sinica Issue 12, (1997)
- 作者机构：
  
  清华大学电子工程系
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN911.4
- Published：1997
- 稿件说明：
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[1]肖承山,冯振明.多维MIMO数字系统的可达性可观测性和噪声格拉姆矩阵[J].电子学报,1997(12):92-95.

肖承山, 冯振明. Reachability, Observability and Noise Gramians of Multidimensional MIMO Digital Systems[J]. Acta Electronica Sinica, 1997, (12).
[1]肖承山,冯振明.多维MIMO数字系统的可达性可观测性和噪声格拉姆矩阵[J].电子学报,1997(12):92-95. DOI：

肖承山, 冯振明. Reachability, Observability and Noise Gramians of Multidimensional MIMO Digital Systems[J]. Acta Electronica Sinica, 1997, (12). DOI：

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．

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.

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