THEORITICAL SYSTEM OF MULTIDIMENSIONAL SYSTEM AND ITS APPLICATION

本课题研究多维系统的理论体系及其在实际系统中的应用，取得了以下成果。(1)稳定性和镇定：传统的稳定性理论和判据依赖于系统的维数。在Grobner基的基础上，研究了与维数无关的新理论和一般准则。(2)实用nD系统：定义了实用nD系统，因为nD系统的一个独立变量的域是有限的。研究了实际nD系统的综合与分析方法，特别是镇定、镇定反馈补偿和最优控制。(3)二维模型跟踪伺服系统：给出了二维模型跟踪伺服问题的两种形式。一种是基于二元多项式环。另一种是状态变量法。(4)应用：将上述结果应用于非单位记忆线性多程过程的控制器设计。最后，用MAPLE开发了新的多维系统CAD系统。

The project deals with theoretical system of multidimensional system and its application to practical systems and has obtained the following results.(1) Stability and stabilization : The conventional stability theory and criterion depends on the system dimension. Here new theory and general criterion, independent on dimension, is studied based on Grobner Bases.(2) Practical nD system : The practical nD system is defined, as the domain of one independent variable of nD system is finite. The synthesis and analysis method of practical nD system, especially stabilization, stabilizing feedback compensatory and optimal control are investigated.(3) 2D model-following servo system : Two formulations of 2D model-following servo problem have been given. One is based on 2 variable polynomial ring. The other one is state variable formulation.(4) Application : The above results are applied to desinging the controller of non-unit memory linear multipass processes. Finaly the new CAD system with MAPLE, for multidimension system is developed.