Disturbance localization and decoupling in stationary linear multivariable systems

In a recent paper, Wonham and Morse [1] have presented geometric conditions for the localization of disturbances in multivariable systems. In this correspondence, some algebraic conditions for this problem are presented. In addition, a state feedback matrix for disturbance localization is presented. Contrary to the result in [1], the conditions presented here are only sufficient. However, they do establish an interesting correspondence between the decoupling and disturbance localization problems for multivariable systems. In fact, it is shown that if the scale matrix for the disturbance satisfies a null space property, then the state feedback matrix of a particular matrix pair which decouples a system localizes its disturbances.