ASYMPTOTIC STABILIZATION OF A CLASS OF SMOOTH 2-DIMENSIONAL SYSTEMS

This paper studies the asymptotic stabilizability of two-dimensional control systems. The class under consideration includes C∞ systems that satisfy a certain genericity assumption and all real analytic systems. Necessary and sufficient conditions for feedback stabilization using continuous feedback and a sufficient condition for C1-feedback stabilization are given. This latter condition is given in terms of an inequality involving two indices. If the direction of the inequality is changed, an obstruction to C∞-feedback stabilizability is obtained. A subclass of polynomial systems is also studied and given complete necessary and sufficient conditions for global asymptotic stabilization using C1-feedback.