About Switched Affine System Interconnected with Fast LTI Dynamics

We study an interconnection between a slow switched affine system and a fast LTI system. The lower dimensional slow and fast subsystems are computed via the singular perturbation approach. We consider the classical stabilization method based on the existence of a stable convex combination (while ignoring the fast dynamics) and we provide an LMI condition for checking ultimate boundedness when the fast dynamics is taken into account. Numerical example illustrates the main result.