ON THE TWO-BLOCK H-INFINITY PROBLEM FOR A CLASS OF UNSTABLE DISTRIBUTED SYSTEMS

摘要

This paper deals with the two-block H-infinity control problem for distributed plants with finitely many unstable modes. We assume that weighting filters in the H-infinity 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(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 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 mu and m(2), whose solutions give the Schmidt pairs of the associated Hankel operator and the functions needed for the parametrization of all the suboptimal solutions, respectively. [References: 28]