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Abstract
This paper focuses on the problem of stabilization of homogeneous systems with dilations using implicit Lyapunov functions. In this paper, we define implicit homogeneous Lyapunov functions and implicit homogeneous control Lyapunov functions. Moreover, we proposed a design method of implicit homogeneous control Lyapunov functions and a controller design method based on the functions. Finally, we confirmed the effectiveness of the proposed method by computer simulation.
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