This article proposes a new high-frequency continuous-time two degrees of freedom (DOF) periodic control scheme to compensate linear time-invariant (LTI), square/nonsquare multivariable plants. The proposed scheme is more effective when the plant is nonminimum phase, or has more inputs than outputs. It is proved that, in averaged sense, the design of periodic controller can be recast as designing a 2-DOF LTI controller for an equivalent LTI plant. The conditions for which this equivalent plant becomes minimum phase are also obtained. When this plant is minimum phase and has no more inputs than outputs, the synthesis of the above-mentioned LTI controller is carried out using an linear matrix inequality-based H-infinity/loop transfer recovery (LTR) approach to achieve linear quadratic regulator (LQR) loop behavior asymptotically. The design method being based on LTR, the reference-input-to-output transfer function of the averaged compensated system becomes same as that using LQR. The periodic controller is shown to exhibit negligible ripples in the plant output, but O(1) ripples in control input. Suitable examples are considered to show the superiority of the proposed control.