On the two-block H∞ problem for a class of unstable distributed systems Original Research Article

This paper deals with the two-block H∞ control problem for distributed plants with finitely many unstable modes. We assume that weighting filters in the H∞ mixed-sensitivity problem are finite-dimensional. Then the corresponding optimal two-block problem can be solved by finding the Schmidt pairs of a Hankel operator whose symbol is of the form m*2(m*1u + û) where image, û set membership, variant H∞, and image and m1 set membership, variant H∞ are inner; and the suboptimal two-block problem can be solved by finding the solutions of certain functional equations very similar to the ones satisfied by the Schmit pairs of the above-mentioned Hankel operator. In this paper a unified approach is proposed for solving both the optimal and suboptimal two-block problems. We obtain two systems of linear equations, expressed in terms of state-space realizations of u and m2, whose solutions give the Schmidt pairs of the associated Hankel operator and the functions needed for the parametrization of all the suboptimal solutions, respectively.