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Nearly time optimal stabilizing patchy feedbacks. (Feedback de type patchy stabilisant en temps presque optimal.) (English) Zbl 1158.93388
Summary: We consider the time optimal stabilization problem for a nonlinear control system \(\dot x=f(x,u)\). Let \(T(y)\) be the minimum time needed to steer the system from the state \(y\in\mathbb R^n\) to the origin, and call \({\mathcal A}(\tau)\) the set of initial states that can be steered to the origin in time \(T(y)\leq\tau\). Given any \(\varepsilon>0\), in this paper we construct a patchy feedback \(u=U(x)\) such that every solution of \(\dot x=f(x,U(x))\), \(x(0)= y\in{\mathcal A}(\tau)\) reaches an \(\varepsilon\)-neighborhood of the origin within time \(T(y)+\varepsilon\).

MSC:
93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
93B52 Feedback control
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