Time-delayed impulsive stabilization of unstable periodic orbits in chaotic hybrid systems

The chapter presents a time-delayed impulsive feedback approach for the stabilization of periodic orbits in hybrid chaotic systems. A rigorous stability analysis of the proposed method is given. By using the proposed time-delayed impulsive feedback method, we consider two special applications. One application is detecting periodic orbits in a special class of hybrid system, a switched arrival system, which is a prototype model of many manufacturing and computer systems where large amount of work is processed at a unit time. The other application considers the stabilization of periodic orbits of chaotic piecewise affine systems, in particular, Chua's circuit, which is another important class of chaotic hybrid systems. Simulations are presented to show the effectiveness of the approach proposed.