Local small time controllability and attainability of a set for nonlinear control system

In the present paper, we study the problem of small-time local attainabilit y (STLA) of a closed set. For doing this, we introduce a new concept of var iations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditio ns are obtained when the considered set is a hyperplane.