Transfer Function Optimization Procedure for the H 2/H ∞ Problem

Abstract

In this paper, the H2/H∞ problem is considered in a transfer-function setting, i.e., without a priori chosen bounds on the controller order. An optimization procedure is described which is based on a parametrization of all feasible descending directions stemming from a given point of the feasible transfer-function set. A search direction at each such point can be obtained on the basis of the solution of a convex finite-dimensional problem which can be converted into a LMI problem. Moving along the chosen direction in each step, the procedure in question generates a sequence of feasible points whose cost functional values converge to the optimal value of the H2/H∞ problem. Moreover, this sequence of feasible points is shown to converge in the sense of a weighted H2 norm; and it does so to the solution of the H2/H∞ problem whenever such a solution exists.