H2/H∞ controller synthesis: illustrative numerical results via quasi-newton methods

A quasi-Newton search technique is applied to the fixed-structure H₂/H_∞ control problem introduced in [1,2]. This quasi-Newton technique is based upon the BFGS variable metric algorithm developed in [3] for unconstrained nonlinear optimization. A barrier modification is used to enforce closed-loop stability, while a discrete homotopy is used to enforce an H_∞ constraint. Numerical results for three different illustrative problems are presented.