DQIT: μ-synthesis without D-scale fitting

In this paper, we propose a new approach for synthesizing robust H_∞ controllers that can avoid the difficulties of D-scale fitting in D-K iteration, and possibly reduce the conservatism due to simplified uncertain models. First, all nominal stabilizing controllers are parameterized by Q-parameters. Each synthesis iteration includes a D-step and a Q-step. In the D-step, optimal D-scaling at each frequency grid point is found as the standard D-K iteration. However, there is no need to fit a parameterized model for D. In the Q-step, the scaled H_∞ problem is approximated by a finite-dimensional optimization problem in the frequency domain, using the D-scaling data directly from the D-step. Numerical examples show significant improvement over the existing approach in certain cases.