On the sensitivity of the H-infinity norm of interconnected systems with time-delays

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 timedelays. In this framework, we analyze the properties of the H-infinity norm of interconnected systems with time-delays. 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 Hinfinity norm for systems with time-delays.