This paper discusses for linear systems the performance limitations imposed when the plant to be controlled is unstable (with RHP-poles). The first limitation is that the plant needs to stabilized using feedback control, and this requires the active use of manipulated inputs. The instability imposes a lower bound on the H₂- and H_∞-norms of the transfer function KS from outputs to inputs. Stabilization may thus be impossible if the input usage, due to measurement noise or disturbances, exceeds the saturation limits. These limitations are independent of the presence of RHP-zeros, but the combination of RHP-poles and RHP-zeros implies further performance deterioration. For a stabilized plant, the instability will manifest itself by the presence of a RHP-zero in the transfer function KS from the output to input used for control, which again imposes performance limitations in terms of the input movement.