ℋ2-Optimal disturbance rejection by measurement feedback: The singular case

This work concerns a new methodology to solve the ℋ2-optimal disturbance rejection problem by measurement feedback in the singular case: namely, when the plant has no feedthrough terms from the control input and the disturbance input to the controlled output and the measured output, respectively. A necessary and sufficient condition for problem solvability is expressed as the inclusion of two subspaces-a controlled-invariant subspace and a conditioned-invariant subspace. Such subspaces are directly derived from the Hamiltonian systems associated to the ℋ2-optimal control problem and, respectively, to the ℋ2-optimal filtering problem. The proof of sufficiency, which is constructive, provides the computational tools for the synthesis of the feedback regulator. A numerical example is worked out in order to illustrate how to implement the devised procedure.