Predominantly, control theory deals with centralized (unrestricted) architectures. However, in practice, decentralized architectures are often preferred. The reasons for this preference are manyfold and include ease of understanding, maintainability, cabling issues and others. The aim of the current paper is to gain insight into the fundamental performance limitations that arise from the use of a decentralized architecture. These fundamental limitations can guide the design of decentralized controllers and offer insight into the performance loss incurred by the use of a restricted architecture. An interesting feature of the results is that they depend, inter-alia, on the relative gain array (RGA). This gives new insight into this standard tool for assessing input-output pairings in decentralized control architectures.