The complexity of modern control systems requires mitigating the effects of numerous anomalies, such as attacks, faults and network-induced disturbances. In this perspective, the synthesis problem of a dissipation block for anomaly-tolerant control is addressed. The dissipation technique consists in interconnecting a block to a system in order to make their interconnection dissipative. The underlying idea is that, if the resulting dissipative characterization is suitably chosen, the considered anomalies can be mitigated. In this paper, it is revealed how the block, here an LTI system, can be synthesized by deriving sufficient LMI-based conditions. A numerical example is provided to illustrate this result which is applied to design a control reconfiguration, providing a defense mechanism that ensures resilience with respect to a data-injection cyber attack.