Abstract
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) |
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Pages (from-to) | 279-310 |
Number of pages | 32 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Volume | 24 |
Issue number | 2 |
DOIs | |
State | Published - 2007 |
All Science Journal Classification (ASJC) codes
- Analysis
- Mathematical Physics
- Applied Mathematics