In this paper new fundamental theorems are stated, which allow to easily determine a first-order majorant system of a pseudo-quadratic uncertain MIMO discrete-time system. For the above class of systems, some results and systematic methods are provided, which allow to solve, “via majorant systemâ€Â, several analysis problems of robust stability, stabilization and tracking of a generic reference signal with bounded variation in presence of a generic disturbance with bounded variation. The utility and the efficiency of the main results proposed in this paper are illustrated with three significant examples.