Stabilizing unstable periodic orbits in higher dimensional systems based on stability transformation method

In this study, we consider stabilizing unstable periodic orbits of a continuous-time chaotic system based on stability transformation method. In previous work, we proposed a procedure which transforms stability of some fixed points embedded in chaotic attractor without information of its location. The procedure is powerful control method to stabilize unknown unstable periodic orbits, however it has considered only simple case such that an 1-dimensional (1-D) map can be used as embedded return map. In this paper, we try to extend our method to higher dimensional and continuous-time systems. As an example, we show a process to stabilize fixed points in 2-D chaotic map and unstable periodic orbits of 4-D chaos generator. By applying the proposed method to unstable fixed points of Lozi map and unstable periodic orbits of a hysteresis chaos generator, we confirm the effectiveness of the method.