非线性系统的局部稳定控制

Local stabilization of nonlinear systems

对一类非线性系统的局部稳定控制问题，首先证明一个四次方程实根判定定理，由此给出一类四次型定号的条件和一类系统局部稳定的充分条件。然后利用以上结论和中心流形的理论给出一类非线性控制系统局部稳定的充分条件。

In this paper, the local stabilization problem of a class of nonlinear control systems is discussed. A theorem concerning the roots of quartic algebraic equations is proved. By using this results we give some sufficient conditions for the local asymptotic stability of a class of nonlinear control systems.