Some estimates pertaining to sensitivity and robust stability of input-output systems

The estimates derived in this paper strengthen the available results on sensitivity and robust stability of input-output systems. Two types of estimates are discussed: the “sensitivity type”, which establishes a bound for the output change when the system is perturbed but the input remains the same, and the “robustness type”, which gives a bound for the output change when the input changes but the perturbation does not. First, estimates for general systems over abstract extended spaces are derived; these results are then applied to (1) two frequently used control configurations, and (2) systems governed by vector integral and differential equations on the time domain 0, ∞). The applications of the estimates are illustrated by several examples. This research was supported by the National Science Foundation under Grant #DMS-9102910