有限网格上一类二维系统的线段能达性和能控性

T.Kaczorek等研究了定义在两条射线组成的区域内通常边界条件下一般奇异模型(GSM)的局部能达性和能控性.本文讨论了有限网格上二维GSM，它是图象处理和工程应用中的另一类边界问题．利用Z变换，我们得到一个定义在矩形区域上的模型的状态响应公式，与有线网格上系统的非因果关系一致，进而定义和研究了线段的能达性和能控性，推广了1，2]关于局部的直线段能达性和能控性的结果．本研究扩大了二维系统模型边界条件类型的应用范围．

Line segment reachability and controllability for a class of 2-D systems defined on a finite grid

T. Kaczorek et al., studied the general singular model (GSM) with the usual boundary conditions defined in a quadrant angle domain as well as its local reachability and controllability. This paper discusses the GSM of 2-D system with a finite grid, which is another class of boundary problems in picture processing and engineering applications. Using finite Z-transform, we derive the state response formula for the model defined on a rectangle. In accordance with non-causal characteristic of the system with finite grid, we define and study line segment reachability and controllability, which generalize the results concerning local and straight line reachability and controllability from 1, 2]. Thus, it is clear that investigation of the model extends types of boundary conditions and application range for 2-D systems is enlarged.