  In a recent work [Manucci, Unger, ArXiv e-print 2404.10511, 2024], the
authors propose using two generalized Lyapunov equations (GLEs) to derive a
balancing-based model order reduction~(MOR) method for a general class of
switched differential-algebraic equations (DAEs). This work explains why these
GLEs provide solutions suitable for MOR by showing that the image set of the
solutions of the two GLEs always encloses the reachable and observable set of a
suitably defined switched system with the same input to output map of the
switched DAE system.
