一类非线性系统的局部镇定及吸引域估计

Local stabilization of a class of nonlinear systems and estimation of region of attraction

研究了一类非线性系统的局部稳定问题,应用中心流形定理,给出了这类非线性系统渐近镇定的充分条件和系统的吸引域估计。设计出镇定系统的反馈控制律,特别研究了一类平面非线性系统,给出了系统镇定的若干条件。通过实例说明选取控制律应注意的一些问题,给出了多个实例,表明结果的有效性。

The problem of local state feedback stabilization of a class of nonlinear systems is studied. Based on the center manifold theory, a sufficient condition of asymptotical stabilization of a class of nonlinear systems and estimation of region of attraction are provided. The feedback control law is designed. The problem of the stabilization for a class of planar nonlinear systems is specially investigated. What problems concerning the choice of the feedback control laws need to be paid attention to is illustrated by examples. Validity of the results is proved with illustrations.