In a previous paper (Bensoussan 1984) we have shown that the sensitivity of a single-input single-output minimum-phase system can be reduced below any given positive value over any finite frequency range of interest while not exceeding a global sensitivity bound on the whole frequency domain. We shall use these results in order to study the problem of decentralized control of weakly coupled plants which is also shown to be strongly linked to the problem of sensitivity reduction to external additive noise applied at the output. We propose a scheme of compensation which applies to a family of weakly coupled plants whose diagonal part is minimum phase.