This article deals with the design of optimal controllers and, as an embedded problem, with the computation of achievable performance bounds in the control of non-minimum phase, unstable multi-input multi-output systems. The cost function comprises a time-weighted measure of the tracking error (ITSE) and an incremental quadratic penalisation of the control effort. The proposed methodology relies on the properties of a frequency domain generalisation of the ITSE index. The solution to the optimisation problem can be computed using orthonormal basis function expansions, and a closed-form expression is found for the optimal coefficients of the expansion. Numerical examples are presented to illustrate the results.