On Variation Bounding System Operators

Bounding or diminishing the number of sign changes and local extrema in a signal is an intrinsic system property in, e.g., low-pass filtering or the over- and undershooting behaviour in the step-response of controlled systems. This work shows how to verify these properties for the observability/controllability operator of a linear time-invariant system under strict external positivity of a set of compound systems, which relaxes/generalizes the standard external positivity notion. In contrast to earlier work, the presented approach is significantly less dependent on a particular realization. The results are demonstrated by bounding the number of sign changes in an impulse response and, thus, the number of local extrema in the step response.