Abstract <p>A new analytical approach to static output feedback pole placement for linear time-invariant systems is proposed, where the system order equals the product of inputs and outputs, and the controllability and observability indices take the maximum and minimum possible values, respectively. This approach uses the Cayley–Hamilton theorem in relation to the matrix of a closed-loop control system. The applicability of the proposed method of static output feedback pole placement is not limited to fourth-order systems with two inputs and two outputs. In addition, the method’s applicability does not depend on whether the system is reducible to modal control by state with fewer inputs or to modal observation with fewer outputs. On the examples of sixth-order multi-input multi-output systems not reducible to systems with fewer inputs or outputs, the process of obtaining analytical solutions to the problem of modal output control, providing desirable pole placement is demonstrated. For systems from the considering class, the obtained solutions are unique.</p>