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In this paper, we propose a two-step controller design method with control Lyapunov functions (CLFs) for nonlinear systems with convex input constraints. In the first step, we derive an input which minimizes the time derivative of a local CLF via nonlinear convex optimization. According to the Karush-Kuhn-Tucker condition (KKT-condition), we clarify the necessary and sufficient condition for the minimizing...
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