Analysis of a controlled 3-D piecewise-constant circuit with time-delayed feedback

In this study, we consider a hysteresis piecewise-constant circuit with feedback of time-delayed states. In general, it is relatively hard to treat a continues-time dynamical system with time-delayed components in theoretical sense. Since the behavior of our proposed system is governed by piecewise-constant vector field, the stability of the system can be analyzed based on the geometric approaches of the phase space. In this paper, we consider a stabilizing control of unstable periodic orbits by time-delayed feedback and analyze the stability. We derive a piecewise linear map to describe the system dynamics in a neighborhood of a periodic orbit and show analytical results on the stability.