电网络的现代系统理论分析——“线性系统几何理论”的应用

Modern System Theory Analysis for Electrical Network:The Application of "Geometric Principle of Linear System"

"现代系统理论"与"现代网络理论"有着紧密的联系。系统理论的概念与方法渗透到网络分析与综合中,可以认为网络理论是受基尔霍夫定律约束的系统理论的子学科。从"经典网络理论"发展到"现代网络理论"是人类对电气技术认识上的飞跃,当前计算技术的飞速发展和多学科的交叉融合,遂给予复杂网络的设计和计算等诸方面带来了深刻的变化。线性系统理论是一个非常活跃的研究领域,由于它对如此众多的实际系统都能给出数学模型,进行优化设计,从而得到了广泛应用。当前由于电路微型化与固体组件的出现,导致"R-C有源网络"应用范围很广。在复杂的线性系统设计中,须在计算机上仿真,其动态方程的"实现"可用"R-C有源网络"的综合方法。"线性系统几何理论"是将线性系统的动态分析转化为状态空间中相应的几何问题,它是通过使用核空间、象空间、不变子空间的概念和方法来实现的。这种几何方法的特点是简洁明了,避免了状态空间中大量繁复的矩阵推演计算,几何理论已应用于观测器与R obust调节器的设计中。

There is a close relation between ＂Modern System Theory＂and＂Modern Network Theory＂. In recent years ,the concepts of system theory has infiltrated into network analysis and synthesis,we may believe the network theory restricted Gilhufu＇s law,is subsidiary discipline of system theory. Linear System Theory is an exciting area of study because of so many real-world application in which a Linear System mathematical model can be used to represent agiven physical system,and obtain optimal design. Now ,the trend to circuit miniaturized and advent of solid-state devices have led to the wide use of ＂Active R-C Network＂. In the design of complicated linear system,it is necessary to obtain the dynamic equations,in order to be simulated through digital computed. For the ＂realization＂ of dynamic equations,synthesis of ＂Active R-C Network＂ could be adopted, ＂Geometric Principle of Linear System＂ is the one that the dynamic behavior analysis is transformed into the correspondent geometric approach in the state space ,the particularity of geometrical principle is brief and clear, and escapes the tremendous complicated matrix calculation. The concepts and methods of kernel space,image space and invariant subspace are used ,and are applied on the designs of observatory and Robust regulator.