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 time-delays. 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 give 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.nrpages: 6status: publishe