Abstract
This paper investigates necessary conditions for feedback stabilizability of nonlinear control systems, which was originally proposed by Coron (1992). The purpose is to provide some detailed and practical descriptions of the conditions, through assuming that equilibria sets of systems form a regular submanifold of their state space. At first, as a special version of the stabilizability condition, it will be shown that a system is not feedback stabilizable if the number of inputs differs from the dimension of the equilibria submanifold. Secondary, we will show that the stabilizability condition can be reduced in a sense if the equilibria set satisfies a certain intersection condition. As a major application of this result, we will show that the stabilizability condition for affine control systems is independent of the input vectorfields.
