New Duality Relations in Linear Systems and Optimal Control under Bounded Disturbances

In this paper, we introduce novel duality relations that complement the well-known invariant ellipsoids method. These relations yield ellipsoids with newly established geometrical interpretations and connections to linear system norms. The established duality leads to the optimal synthesis results for state-feedback control, filtering, and output-feedback control problems in the presence of bounded disturbances. The proposed output-feedback control solution is demonstrated to be optimal and surpass prior sub-optimal results.