We consider the time optimal stabilization problem for a nonlinear control system over(x, ̇) = f (x, u). Let T (y) be the minimum time needed to steer the system from the state y ∈ Rn to the origin, and call A (τ) the set of initial states that can be steered to the origin in time T (y) ≤ τ. Given any ε > 0, in this paper we construct a patchy feedback u = U (x) such that every solution of over(x, ̇) = f (x, U (x)), x (0) = y ∈ A (τ) reaches an ε-neighborhood of the origin within time T (y) + ε.
|Original language||English (US)|
|Number of pages||32|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - Jan 1 2007|
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Applied Mathematics