General consideration for modelling and analyzing switched dynamical systems

Previously, switched dynamical systems have been studied in terms of switching that 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 currentmode 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 covered by this modelling and analytical method.