A geometric perspective on H2-optimal rejection by measurement feedback in strictly-proper systems: the continuous-time case

In this work, we develop a geometric method for solving the problem of H2-optimal rejection of disturbance inputs in continuous-time linear systems without feedthrough terms from the control input and the disturbance input to the controlled output and the measured output. A necessary and sufficient condition for the solvability of the problem is expressed in terms of a pair of subspaces, a controlled-invariant subspace and a conditioned-invariant subspace, derived from the Hamiltonian systems associated with the problem. The if-part of the proof shows how to synthesize the feedback regulator, which is non-strictly-proper in general.