Almost Disturbance Decoupling via static state feedback with pole placement: A geometric approach

This contribution focuses on solving the Almost Disturbance Decoupling Problem (ADDP) via static state feedback and simultaneously placing system poles. It is shown that, when solving ADDP by means of high gain state feedback, in any solution are present some fixed finite poles and infinite poles in the closed loop system, which can not be freely assigned. A class of “optimal” geometric subspaces with which maximal complementary pole placement can be achieved is characterized. A reliable construction algorithm for such an optimal (or suboptimal) geometric subspace (resp. the state feedback solution) is also proposed for general case. An example is proposed to illustrate our contributions. It should be noted that all the contributions are based on geometric control theory.