Model reduction of hybrid switched systems

A hybrid dynamical system is a system described by both differential equations (continuous flows) and difference equations (discrete transitions). It has the benefit of allowing more flexible modeling of dynamic phenomena, including physical systems with impact such as the bouncing ball, switched systems such as the thermostat, and even the internet congestion as examples. Hybrid dynamical systems pose a challenge since almost all reduction methods cannot be directly applied. Here we show some recent developments in the area of model reduction of switched dynamical systems.