非线性控制系统的最小实现

MINIMAL REALIZATION OF NONLINEAR CONTROL SYSTEMS

对于那些由代数微分方程描述的具有输入输出关系的非线性控制系统，本文采用两种方法讨论了其最小实现问题：一种方法是直接计算系统的特征列；另一种方法则采用了本原元定理．两种方法给出的最小实现所需的状态变量最小数目是相等的．

For those nonlinear control systems described by a set of algebraic differentialequations in input and output, two methods are used to discuss their minimal realizationproblems. One makes use of characteristic set to determine the order of a system, i.e. theminimal number of the states required. The other uses primitive element theorem and resolventtheory. By obtaining the minimal order and the minimal degree of an algebraic differentialpolynomial annuled by the primitive element, the minimal realization of the system can begiven. Some amount of manipulation can be completed by using mathematic mechanization.