Homogeneous Stabilizing Feedback Laws

A machinery is developed for the explicit construction of lo cally H older continuous feedback laws that asymptotically stabilize highly nonlinear single input control systems Actively employing symmetries here families of dilations of nilpotent approximating systems the problem is basically reduced to questions about relative locations and intersection properties of certain varieties in a lower dimensional space typically n dimensional projective space Special consideration is given to the three di mensional case with explicit examples a discussion of Brockett s condition and a new necessary condition for the existence of continuous homogeneous feedback laws that asymptotically stabilize

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