多输入下三角系统的几何描述

Geometric characterization of multi-input lower-triangular forms

针对多输入情形,考虑非线性系统通过坐标变换和状态反馈等价于下三角系统的问题.首先给出了多输入下三角非线性系统的两种基本形式.利用奇异分布的有关理论,给出了多输入非线性系统通过反馈等价于非自治下三角形式系统的充要条件.借助算法说明了如何通过状态反馈和坐标变换实现上述系统间的等价转换.

This paper is concerned with the problem as to whether a multi-input nonlinear system is equivalent to the so-called low-triangular form.Two elemental forms of multi-input lower-triangular systems are proposed. Then,using the theory of singular distributions,the necessary and suffcient conditions under which multi-input nonlinear systems are locally feedback equivalent to these two lower-triangular systems are established.Furthermore,algorithms are provided to describe how to realize these equivalent transformations via state feedbacks and coordinate conversions.