An exterior-point approach to the mixed H2=H∞ control problem

The purpose of this paper is to propose an exterior-point approach to the mixed H₂/H_∞ control problems using a partial derivative of the H2 cost function. The main contribution of this paper is to give an iterative method for obtaining a feasible solution of the problem, which produces a sequence of controller variables from the infeasible region to the feasible one. This approach has the property such that any stabilizing controller can be used as an initial point. The efficiency of our approach is shown by a numerical example which cannot be solved with the common Lyapunov variable method.