Fundamental limitation on achievable decentralized performance

A commonly accepted fact is that the diagonal structure of the decentralized controller poses fundamental limitations on the achievable performance, but few quantitative results are available for measuring these limitations. This paper provides a lower bound on the achievable quality of disturbance rejection using a decentralized controller for stable discrete time linear systems with time delays, which do not contain any finite zeros on or outside the unit circle. The proposed result is useful for assessing when full multivariable controllers can provide significantly improved performance, as compared to decentralized controllers. The results are also extended to the case, where the individual subcontrollers are restricted to be PID controllers.