Averaging in singularly perturbed hybrid systems with hybrid boundary layer systems

We analyze a class of singularly perturbed hybrid systems based on two auxiliary hybrid systems: the averaged system, which approximates the slow dynamics, and the boundary layer system, which approximates the fast dynamics. The average system is generated by averaging the solutions of the boundary layer system. The novelty of this work is that the boundary layer system is a hybrid system rather than a continuous-time system. This extends available results to cover new classes of hybrid systems. We illustrate how to apply our results through an example that is a power converter system under hybrid feedbacks implemented by pulse-width modulation (PWM).