一类非线性系统的全局镇定

Global stabilization for a class of nonlinear systems

研究一类非线性系统的全局镇定问题,对一类四阶非线性系统,利用系统的静态稳定性导出了系统的动态稳定性,提出了镇定这类系统的反馈控制律的设计方法,并获得了这类系统全局镇定的充分条件.将所得的方法推广到具有一般性的一类非线性系统中.设计出镇定这类非线性系统的反馈控制律,并证明了在适当条件下闭环系统是全局渐近稳定的.

The problem of global stabilization for a class of nonlinear systems is considered. Firstly, the dynamic stability is educed from the static stability for a class of forth-order nonlinear systems. The new designed method of feedback control law, which globally stabilized the systems, is proposed, and the sufficient condition for the global stabilization of the systems is obtained. Then, the method is extended to more generally nonlinear systems and the feedback control law, which globally stabilized the systems, is designed. It is shown that the nonlinear closed-loop systems can achieve the global asymptotic stability under the adaptive conditions.