This paper considers the servomechanism problem for linear multivariable systems in the state space setting. In this paper are given: (i) necessary and sufficient conditions for a given plant satisfying the steady-state criteria, i. e., possing the property to regulate the outputs to obey reference commands despite disturbance input, (ii) a necessary and sufficient condition for the existence of a dynamic compensator such that the composite system of this and the given plant is observable and satisfies the steady-state characteristics, and (iii) a simple algorithm with matrix operations for the minimal-order dynamic compensator design. A useful design procedure for linear multivariable servomechanisms, which consists of the compensator design for the steady-state characteristics and the regulator design for the transient characteristics, is also shown by using the above results.