New Dualities in Linear Systems and Optimal Output Control under Bounded Disturbances

In this paper, we introduce novel equations that are dual to the ones of the well-known invariant ellipsoids method. These equations 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.