一类非线性系统的局部镇定

THE LOCAL STABILIZATION OF A CLASS OF NONLINEAR SYSTEMS

研究一类非线性系统的局部状态反馈镇定问题．基于中心流形理论,给出一类非线性系统渐近镇定的充分条件,并设计出镇定系统的反馈控制律．文中利用具有齐次导数的Lyapunov函数方法,特别研究了一类平面非线性系统及具有二重零特征值的一类非线性系统的渐近镇定问题,给出了系统镇定的若干充分条件,并构造出控制律．文中的例表明了所得结果的有效性．

In this paper, the problem of local state feedback stabilization of a class of nonlinear systems is considered. Based on the center manifold theory, a sufficient condition of asymptotical stabilization of a class of nonlinear systems is given, and the control law, which stabilizes the nonlinear systems, is designed. Using the method of Lyapunov function with homogenous derivative, we investigate specially the problem of the stabilization for a class of planar nonlinear systems and a class of nonlinear systems with zero eigenvalue of.multiplicity 2, respectively. Some sufficient conditions for stabilization are established, and the control laws are constructed. Some examples are given which show the validity of the results.