On H2-optimization with stable controllers

The problem of obtaining the H2-optimal stable feedback controller for a general optimality criterion is considered. It is shown that this optimization reduces to finding the "best" function in RH2 (i.e. of minimum norm) that satifies an avoidance constraint. A design procedure is proposed for obtaining an optimal stable controller that minimizes the performance index and maintains internal stability. Given an initial point, this is achieved by minimizing a nonlinear objective function subject to nonlinear inequality constraints via a sequential gradient programming method.