A method for the synthesis of interactions in a multivariable system is proposed. The objective of the method is that of utilizing interactions advantageously in the control of multivariable systems. The method ensures the improvement of the performance of the system in a realistic and changeable environment. To effect a description of the environment, the inputs are regarded as belonging to an appropriate function space in the case of the deterministic problem. A vector space of statistical characteristics is utilized for statistical problems. The concept of the interacting domain is introduced to indicate the subset of the input space for which the superiority of the interacting system is guaranteed. Conditions for the existence of several types of interacting domains for linear systems are derived analytically and expressions for their boundaries are obtained. An experimental procedure is proposed for determining the interacting domains without reference to (oi knowledge of) the equations of the system. Several examples are discussed and further research areas in this direction are indicated.