一类不确定非线性系统的鲁棒稳定控制器的设计

运用微分流形的分布为工具，先将一类多输入多输出不确定非线性系统通过对角状态反馈变换为一个状态矩阵为区间矩阵的不确定线性系统，把非线性系统的不确定性和对角状态反馈变换误差转化为区间矩阵。再对区间矩阵系统应用实对称矩阵集合的最小上界定理进行鲁棒控制器设计，从而达到对原非线性系统的鲁棒稳定控制。最后通过一个算例验征了该方法的有效性。

Design of Robust Stabilization Controller for a Class of Nonlinear Systems

A discussion is devoted to the design of robust stable controller for a class of uncertain nonlinear systems in this paper.The uncertain nonlinear system is transformed to an interval matrix system based on the tool of distribution of differential manifold and feedback linearization. The uncertainty of the nonlinear system and the error of the feedback linearization are transformed to an interval matrix.The robust stable controller is designed with the minimum upper bound theorem of the real symmetric matrix set for the interval matrix system.The designed controller can make the uncertain nonlinear system robust stable.An example is given to validate the availability of this method.