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本文的目的是描述与分析非线性控制系统的拓扑结构.文中首先定义可线性化系统,然后引入Whitney拓扑,并用此定义非线性控制系统族上的拓扑.在这个拓扑下,证明了除单输入二维系统外,在一般情况下能线性化的系统是一个零测集.最后讨论一般反馈线性化问题.对输入数仅比系统维数少一的情况给出了充要条件,并证明了在此情况下几乎所有的系统均可线性化.
The purpose of this paper is to describe and analyze the topology of a nonlinear control system. First we define a linearizable system, and then introduce the Whitney topology and use it to define the topology of a family of nonlinear control systems. Under this topology, Two-dimensional system, under normal circumstances can be linearized system is a zero-measurement set.Finally, the general feedback linearization problem is discussed.The sufficient and necessary conditions are given for the case that the input number is only one less than the system dimension, In this case, almost all systems can be linearized.