一类非线性系统的反馈非线性化镇定

 给出了一类非线性系统的状态反馈非线性化镇定的方法。首先构造一个人为的输出映射，使得系统的零动态渐近稳定并具有向量相对阶｛1，…，1｝；然后构造一类控制器使得零输出流形服从一类指数稳定的非线性动态方程。利用非线性H∞－控制一个基本结果证明了在较弱的条件下，所得到的闭环系统是局部渐近稳定的。最后以刚体姿态控制为例，说明了利用上述结果，可以得到一类仅仅需要知道系统惯性矩阵元素相对值的反馈方案，从而在一定程度上克服了反馈线性化方法需要精确知道系统参数的弱点。

STABILIZATION OF A FAMILY OF NONLINEAR SYSTEMS VIA FEEDBACK NONLINEARIZATION

An approach to stabilize a family of nonlinear systems via feedback nonlinearization is presented. A dummy output mapping is constructed so that the zero dynamics are made asymptotically stable and the system is of relative degree{1,…,1};then a group of controllers are designed that guarantee the exponential attractivity of the zeroing output manifold. Using tools in nonlinear H ∞ control theory, it is shown that under mild conditions, the resulting closed loop system is locally asymptotically stable. Finally, these results are used to the attitude control problem for a rigid body to design detumbling controllers that only require knowledge of relative value of the system inertial parameters. This technique seems attractive in that, to a certain extent, it may lessen the need of precise system knowledge required by the feedback linearization technique.