Abstract
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 existings, through assuming that equilibria sets of systemsn 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 is less than the dimension of the equilibria submanifold. Secondly, in the case of affine control systems, the stabilizability condition will be shown to be independent of input vectorfields. Finally, as a generalization of the second result, we will show that the condition is decomposed to a pair of parts if the equilibria submanifold has a certain product structure.
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