广义2-D系统Roesser模型的可接受输入序列研究  

Acceptable Input Sequences for Singular Roesser Model of 2-D Linear Systems

作　　者：赵胜民[1] 陆昌根[2] 刘则毅[1] 

机构地区：[1]天津大学数学系,天津300072 [2]南京航空航天大学空气动力学系,南京210016

出　　处：《南京航空航天大学学报》2000年第6期672-676,共5页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：国家自然科学基金(编号:79500012)资助项目

摘　　要：通过将有限矩形上的广义 2 - D Roesser模型转化为等价的代数方程 ,给出了有限矩形上所有输入均为该系统的可接受输入的充要条件 ;利用 2 - D Z-变换以及多项式矩阵的性质 ,给出了无限矩形上所有输入均可接受的充要条件。证明了当系统的输入矩阵行满秩时 ,只要系统在某个有限矩形上的所有输入均为可接受输入 ,则在无限矩形上的所有输入也均为可接受输入。基于矩阵的初等行变换 ,提出了确定广义 2 - D系统 Roesser模型可接受输入序列集合的方法。Two dimensional (2 D) systems are utilized in various practical areas such as image processing, digital data filtering, etc. The singular Roesser model (SRM) is one of the most popular state space models of 2 D linear discrete systems. The SRM may not have a solution for all input sequences. This paper focuses on the acceptable input sequences of the SRM. After transforming the SRM on a finite rectangle into an equivalent algebra equation, sufficient and necessary conditions for all input sequences on the finite rectangle being acceptable for the system are given. By taking 2 D Z transform of the system and using the property of polynomial matrices, sufficient and necessary conditions for all input sequences on the infinite rectangle being acceptable are established. It is shown that all input sequences on some finite rectangle being acceptable for the SRM implies all input sequences on the infinite rectangle being acceptable when the input matrix of the system has full row rank. Based on elementary row operations on matrices, a method for determining the set of acceptable input sequence is proposed. An illustrative example is included.

关 键 词：状态空间 离散系统 控制问题 2-DRoesser模型 2-DZ-变换 

分 类 号：O231.1[理学—运筹学与控制论] TP13[理学—数学]