Intermittent Redesign of Analog Controllers via the Youla Parameter

TL;DR

This paper presents a method for redesigning analog controllers to work effectively with irregular, unknown sampling patterns while maintaining stability and near-optimal performance, simplifying implementation.

Contribution

It introduces a constructive algorithm for redesigning stabilizing controllers that preserves stability and achieves near-optimal performance under unknown sampling patterns.

Findings

Redesign algorithm preserves closed-loop stability.

Achieves near-optimal $H^2$ and $H^inity$ performance.

Uniform sampling is shown to be optimal under fixed sampling density.

Abstract

The paper studies digital redesign of linear time-invariant analog controllers under intermittent sampling. The sampling pattern is only assumed to be uniformly bounded, but otherwise irregular and unknown a priori. The contribution of the paper is twofold. First, it proposes a constructive algorithm to redesign any analog stabilizing controller so that the closed-loop stability is preserved. Second, it is shown that when applied to (sub)optimal $H^2$ and $H^\infty$ controllers, the algorithm produces (sub)optimal sampled-data solutions under any a priori unknown sampling pattern. The proposed solutions are analytic, computationally simple, implementable, and transparent. Transparency pays off in showing the optimality, under a fixed sampling density, of uniform sampling for both performance measures studied.