Sufficient Conditions for Small Time Local Attainability for a Class of Control Systems

We deal with the problem of small time local attainability (STLA) for nonlinear finite-dimensional time-continuous control systems. More precisely, given a nonlinear system x˙ (t) = f(t, x(t), u(t)), u(t) ∈ U, possibly subjected to state constraints x(t) ∈ Ω and a closed set S, our aim is to provide sufficient conditions to steer to S every point of a suitable neighborhood of S along admissible trajectories of the system, respecting the constraints, and giving also an upper estimate of the minimum time needed for each point near S to reach S