| Universal formulas for CLF's with respect to Minkowski balls (1999) | |||||||||||||||
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| This note provides explicit, algebraic stabilizing formulas for clf's when controls are restricted to certain Minkowski balls in Euclidean space. Feedbacks of this kind are known to exist by a theorem of Artstein, but the proof of Artstein 's theorem is nonconstructive. The formulas are used to construct approximation solutions to some stabilization problems. 1 Introduction Smooth control-Lyapunov functions (clf's) provide foundations for much of current feedback control design. See for instance the appropriate sections in the textbooks [2, 6]. The theory of smooth clf's had its origins in Artstein's paper [1]. A very useful characteristic of clf's is the existence of `universal formulas' for stabilization, as described in [5] and the above textbooks. This note continues the search, started in [3] (and continued in [4]), for universal clf formulas for constrained controls. By a universal formula one means, informally (with precise definitions given later), an expression for a stabil... | |||||||||||||||
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