A bound on closed-loop performance based on finite-frequency response samples

A new, computationally tractable, bound is derived for the level of closed-loop performance achieved by a given finite-dimensional feedback compensator with a plant for which a finite number of frequency response samples are computable. The bound involves quantities reflecting the performance of the controller with a finite-dimensional, nominal model of the plant, quantities that can be determined from the finite number of frequency response samples of the true plant, and quantities related to the complexity (in the sense of Vinnicombe) of all systems involved. This bound can be used to 'validate' closed-loop performance in the case that the true plant frequency response samples are of a plant which is not completely known or, to measure the performance of a finite-dimensional controller with a computationally intractable (e.g. infinite-dimensional) model of the true plant.