On the realizability of dynamic precompensators in linear multivariable systems

The problem of static state feedback realization of dynamic full column rank precompensators on a controllable linear multivariable system in a structural framework is considered in this paper. Necessary and sufficient conditions for the existence of a nonregular static state feedback that realize the compensator are stated in terms of the zero-pole structure of the compensator, and the modes and the row image of the controllability matrix of the compensated system. Based on these conditions a formula is presented to find the state feedback matrices realizing a given full column rank compensator. We also show that the corresponding state feedback is unique if and only if the closed loop system is controllable.