Nondiminishing disturbance rejection in linear multivariable systems

This paper presents a constructive procedure for the synthesis of linear multivariable systems whose partial state is corrupted by an unknown nondiminishing disturbance. The system zeros and the unstable modes of the disturbance are assumed to be disjoint. A stable desired closed loop transfer matrix is obtained which can be expressed as the product of an open loop transfer matrix and any proper rational transfer matrix. Internal model principle is employed to realize the closed loop transfer matrix while simultaneously eliminating the effect of steady state disturbance at the output. The controller simultaneously ensures: 1) disturbance decoupling, 2) complete and arbitrary closed loop pole placement, and 3) internal stability. The compensation scheme is presented in the frequency domain.