A design method for fixed-order H∞ controllers via bilinear matrix inequalities

We deal with fixed-order H_∞ controller design problems, based on bilinear matrix inequalities. BMI problems are nonlinear, non-differentiable and nonconvex, and therefore very difficult numerically to obtain global solutions. First, we convert BMI problems into differentiable problems introducing so-called shift-parameters. Next, combining the shift-parameter scheme with quasi-Newton methods, a computational technique has been proposed as BMI solvers. Lastly, we demonstrate the effectiveness of our approach by simulations, with applications to the design of fixed-order H_∞ controllers