A variant of the synthesis method for controlling a linear MIMO system by an output vector is developed that provides the given spectrum of a multidimensional dynamic system in the state space. It is based on the principle of duality of the task of controlling a MIMO system by a state vector and the task of constructing a state observer. The algorithm, without any changes, is applicable for both continuous and discrete cases of describing the mathematical model of the MIMO system, has no restrictions on specifying the spectrum’s elements of the closed MIMO system, and allows us to obtain synthesis problems in analytical form and to parameterize the set of equivalent control laws with feedback. An example of an analytical synthesis of the control law of a hypothetical aircraft is given.