  We consider delay differential algebraic equations (DDAEs) to model
interconnected systems with time-delays. The DDAE framework does not require
any elimination techniques and can directly deal with any interconnection of
systems and controllers with time-delays. In this framework, we analyze the
properties of the H-infinity norm of systems described by delay differential
algebraic equations. We show that the standard H-infinity norm may be sensitive
to arbitrarily small delay perturbations. We introduce the strong H-infinity
norm which is insensitive to small delay perturbations and describe its
properties. We conclude that the strong H-infinity norm is more appropriate in
any practical control application compared to the standard H-infinity norm for
systems with time-delays whenever there are high-frequency paths in control
loops.
