Chaotifying a stable linear controllable system by single input state feedback

In this paper, an approach for chaotifying a stable controllablelinear system via single input state-feedback is presented. Theoverflow function of the system states is designed as thefeedback controller, which can make the fixed point of theclosed-loop system to be a snap-back repeller, thereby yieldschaotic dynamics. Based on the Marotto theorem, it provestheoretically that the closed-loop system is chaotic in thesense of Li and Yorke. Finally, the simulation results are usedto illustrate the effectiveness of the proposed method.