一类多输入不确定非线性系统的镇定

Stabilization of a class of multi-inputs uncertain nonlinear systems

运用非线性系统的精确线性化方法和Ｌｉｅ代数工具，将一类满足一定条件的多输入不确定仿射型非线性系统交换成含可变参数的多变量线性系统。然后通过应用Ｒｏｕｔｈ算术求得合理的状态反馈矩阵，使得不确定向量在给定范围内任意变化时变参数闭环线性系统的特征多项式恒为Ｈｕｒｗｉｔｚ多项式，从而使该线性系统稳定。与此同时，间接地解决了原多输入不确定非线性系统的镇定问题，并且求得了镇定控制律的解析表达形式。给出了一个设计例子，其数值仿真的结果验证了本文所提出方法的正确性和有效性。

A class of multi-inputs uncertain affine nonlinear systems, which satisfy some conditions, are transformed into multi-variable linear systems with variable parameters through the exact linearization method and the tool of Lie algebra. Then the Routh algorithm is used to select the appropriate state feedback matrixes so as to make the characteristic polynomials of the closed loop linear systems be Hurwitz polynomials, while the uncertain variable within variable within their given scopes arbitrarily. Thus the linear systems are stabilized. In this way, the stabilization problem of the original systems is solved and the control laws in analytic form are obtained. The correctness and effectiveness of themethod presented in this paper are illustrated by an example and its simulation results.