Improved IQC description to analyze interconnected systems with time-varying time-delays

Abstract

In this paper integral quadratic constraints (IQCs) are used for robust stability analysis of interconnected systems with uncertain time-varying interconnection topology, that may encompass uncertain time-varying delays. In contrast to previous results frequency weighted multipliers are used that are known to decrease the conservatism enormously. To apply those, the swapping lemma known from adaptive control is used to deal with time-varying uncertainties. These have no Fourier transforms and thus do in general not commute with any weighting functions of the multipliers. Moreover, it is possible to incorporate bounds on the rate of change of the interconnection topology, if they exist, to reduce conservatism even further, when the interconnection is known not to vary arbitrarily fast or to be constant but uncertain.