A descent transfer function procedure for the H2/H∞ problem

In this paper, the H₂/H_∞ problem is considered in a transfer-function setting, i.e., without a priori chosen bounds on controller order. A descent procedure is described which is based on an explicit parametrization of all feasible and descent directions stemming from a given point on the boundary of the feasible transfer-function set. A search direction at each such point can be obtained as the solution of a convex finite-dimensional problem which can be converted into a LMI problem. The procedure in question keeps generating feasible points with decreasing cost values unless the global optimal is attained.