The disturbance decoupling problem with stability constraint and pole placement is examined in a geometric framework. Two types of reduced-order compensators are proposed: one based on the observation scheme, the other on the dual-observation scheme. The novelty lies mainly in these points: (1) the avoidance of eigenspace computations in the syntheses as they rely on the determination of the maximum controlled invariant contained in a given subspace and its dual, i.e. the minimum conditioned invariant containing a given subspace, and pole assignability; and (2) the concerted use of controlled and conditioned invariants, which leads to a straightforward synthesis and also allows a clear interpretation of the dual compensation.
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