General consideration for modeling and bifurcation analysis of switched dynamical systems

In much of the previous study of switched dynamical systems, it has been assumed that switching occurs at a common border between two regions in the same space as the system trajectory crosses the border. However, models arising from this consideration cannot cover systems whose trajectories do not actually "cross" the border. A typical example is the current-mode controlled boost converter whose trajectory is "reflected" at the border. In this paper, we propose a general method to model switched dynamical systems. Also, we suggest an analytical procedure to determine periodic solutions and their stability. The method is developed in terms of solution flows, and no solution has to be explicitly written. Most practical switched dynamical systems can be modeled and analyzed by this method.