Smooth frequency domain parametric optimization in loop-shaping control

This paper presents two tools for frequency domain parametric optimization. The first tool is an approximation of the square of the largest singular value. This approximation works for complex matrices and enables using smooth constrained optimization methods, like sequential quadratic programming, in the multi-input-multi-output control system design. The second tool is a cost effective controller parametrization, which is based on the Hilbert transform. We also give a simple example to help the reader to get started with this synthesis framework.