A general framework for the design of multivariable control systems subject to hard constraints on each control channel is developed. The design procedure is an extension of the well-known H∞ Loop Shaping Design Procedure and is based on the calculation of the maximum possible control amplitude for a certain class of reference signals. Special attention is given to the adaption of the design weights in order to meet the prescribed bounds on the control signal. A multivariable simulation example, the control of the vertical dynamics of an aircraft, illustrates the suggested procedure.