ON THE 2-BLOCK H-INFINITY PROBLEM FOR A CLASS OF UNSTABLE DISTRIBUTEDSYSTEMS

This paper deals with the two-block H-infinity control problem for dis tributed plants with finitely many unstable modes. We assume that weig hting filters in the H-infinity mixed-sensitivity problem are finite-d imensional. Then the corresponding optimal two-block problem can be so lved by finding the Schmidt pairs of a Hankel operator whose symbol is of the form m(2)(m(1)*mu + <(mu)over cap>) where mu is an element of RH(infinity), <(mu)over cap> is an element of H-infinity, and m(2) is an element of RH(infinity) and m(1) is an element of H-infinity are i nner; and the suboptimal two-block problem can be solved by finding th e solutions of certain functional equations very similar to the ones s atisfied by the Schmit pairs of the above-mentioned Hankel operator. I n this paper a unified approach is proposed for solving both the optim al and suboptimal two-block problems. We obtain two systems of linear equations, expressed in terms of state-space realizations of mu and m( 2), whose solutions give the Schmidt pairs of the associated Hankel op erator and the functions needed for the parametrization of all the sub optimal solutions, respectively.