一类不确定非线性系统的鲁棒镇定

Robust Stabilization of a Class of Uncertain Nonlinear Systems via State Feedback

讨论了在自由系统和输入通道都带有有界不确定性的仿射非线性系统的鲁棒镇定问题．借助ＨａｍｉｌｔｏｎＪａｃｏｂｉ不等式（线性系统控制中常用的Ｒｉｃａｔｉ不等式的类比），给出了状态反馈控制设计方法，使对所有允许的不确定性它能镇定该系统．本文指出如果一个相应的ＨａｍｉｌｔｏｎＪａｃｏｂｉ不等式有非负光滑解，则该不确定仿射非线性系统可鲁棒镇定．

The robust stabilization problem of a class of affine nonlinear systems with normbounded uncertainties is discussed for both free system and input matrices. By utilizing HamiltonJacobi inequality we present a state control design which stabilizes the plant for all admissible uncertainties. That is,where a HamiltonJacobi inequality has nonnegative smooth solution there is a robust controller which stabilizing the uncertain nonlinear systems.