Minimum Projection Method for Asymptotic Stabilization of Compact Set

摘要

In this paper, we elucidate the fact that for a continuous differential equation, an asymptotically stable set is homotope to the state space on which the differential equation is defined. Then, we define locally semiconcave practical control Lyapunov functions for stabilization of compact sets and sample stability of the set. Moreover, we propose Minimum Projection Method for stabilization of compact sets and a static discontinuous feedback controller that sample stabilizes a compact set. The effectiveness of the proposed method is confirmed by computer simulation.