H-Infinity Optimal Decentralized Matching Model Is Not Always Rational

TL;DR

This paper demonstrates that in certain structured H-Infinity optimal model matching problems, the optimal solution can be non-rational, challenging the assumption that optimal solutions are always rational.

Contribution

It constructs specific examples showing that the optimal solution to structured H-Infinity problems may be non-rational, despite having rational problem data.

Findings

Optimal solutions can be non-rational in structured H-Infinity problems.

Rational solutions may not always achieve the maximal lower bound of the cost.

Non-rational solutions can reach the same optimal cost as rational ones.

Abstract

We construct structured H-Infinity optimal model matching problems with rational coefficients, in which the optimal solution is not rational, in the sense that the cost does not achieve its maximal lower bound on the set of rational matching models, but the same maximal lower bound can be reached by using a continuous non-rational matching model.