On the sensitivity of the H∞ norm of systems described by delay differential algebraic equations

Abstract

AbstractWe 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∞ norm of systems described by delay differential algebraic equations. We show that the standard H∞ norm may be sensitive to arbitrarily small delay perturbations. We introduce the strong H∞ norm which is insensitive to small delay perturbations and describe its properties. We conclude that the strong H∞ norm is more appropriate in any practical control application compared to the standard H∞ norm for systems with time-delays whenever there are high-frequency paths in control loops.