This article addresses the design of decentralised regulators which supply the control systems with signal tracking and disturbance rejection. This property has to be attained, to the maximum possible extent, even when instrumentation faults occur, thus causing the opening of some feedback loops. The problem is tackled for LTI asymptotically stable plants, subject to perturbations, under the assumption that the Laplace transforms of the exogenous signals have multiple poles on the imaginary axis. The proposed regulator is composed of an LTI nominal controller supervised by a reconfiguration block. Once the actions of the reconfiguration block have been settled, the synthesis of the nominal controller is reformulated as a suitable regulation problem. A constructive sufficient condition for its solvability is established. This condition turns out to be also necessary if the exogenous signals are polynomial in time.