Nonsmooth optimization for multiband frequency domain control design

Multiband frequency domain synthesis consists in the minimization of a finite family of closed-loop transfer functions on prescribed frequency intervals. This is an algorithmically difficult problem due to its inherent nonsmoothness and nonconvexity. We extend our previous work on nonsmooth H∞H∞ synthesis to develop a nonsmooth optimization technique to compute local solutions to multiband synthesis problems. The proposed method is shown to perform well on illustrative examples.