The authors propose a controller design method for linear multivariable systems with periodic inputs. The periodic inputs may have different periods in different input channels. The plant is assumed to be minimum phase but may be unstable. In addition to achieving closed-loop stability and input-output decoupling, the design is to satisfy prespecified bounds on relative steady-state tracking error and sensitivity function. The paper shows that, for minimum phase plants, it is possible to achieve arbitrarily small sensitivity over large bandwidth and arbitrarily small (integral square) tracking error for piecewise continuous periodic inputs in each channel. The paper proposes a design algorithm and gives an illustrative example.