Condensed structural solutions to the disturbance rejection and decoupling problems with stability

Abstract

In this paper, it is shown that a static state feedback control law rejects the disturbance and simultaneously performs input-output decoupling, while ensuring internal stability of the closed loop system, if and only if an integer equality holds for the global undisturbed system and the row subsystems of the combined plant (where the disturbance is handled as a control input), namely in terms of their respective total contents (sums of the orders of the multiplicities of its infinite and finite unstable invariant zeros).