SUMMARYA control system synthesis method for a multi-input and multi-output system with input dead time, input variable constraints, and state variable inequality constraints is described. A practical control algorithm which is suitable for microprocessor implementation is derived from the method and is applied to an induction motor control problem. Good simulation results are obtained, although the designed control system is suboptimal. The control system configuration designed by this method is explained clearly. It is proved that integral actions as well as proportional actions are introduced so as to guarantee good steadystate characteristics in spite of parameter variations of the controlled object. Moreover, a kind of derivative action is introduced to compensate for input dead time effects.