Evaluating the delay robustness of interconnected passive systems with a frequency-dependent integral quadratic constraint

We consider interconnections of output strictly passive systems and study their robustness in the presence of delay. We establish a new integral quadratic constraint (IQC), which captures the magnitude roll-off at high frequencies. The benefit of the roll-off IQC is exemplified in a study of the stability of a cyclic interconnection structure. When used in conjunction with the IQC describing passivity, we obtain a stability bound on the gain that depends on the size of the delay and relaxes a small-gain bound.