On time-domain multiplier criteria for single-input single-output systems

In this note we consider the problem of obtaining time-domain multiplier stability criteria. We show that in the case of single-input single-output systems, time-domain versions of classical frequency domain multiplier criteria can be obtained in a straightforward manner. In many cases, the time-domain criteria are more compact and more readily verified than the original criteria. Our results show that conventional constraints on the frequency response of a transfer function become simple eigenvalue evaluations in the time-domain.