1998 Volume 11 Issue 10 Pages 554-567
In this paper, we deal with fixed-order H∞ controller design problems, based on bilinear matrix inequalities. BMI problems are nonlinear, non-differentiable and non-convex, and therefore very difficult to obtain global solutions numerically. First, we convert BMI problems into differentiable problems introducing so-called shift-parameters. Next, combining the shift-parameter scheme with quasi-Newton methods, we propose a new computational technique as BMI solvers. Lastly, we demonstrate the effectiveness of our approach by simulations, with applications to the design of fixed-order H∞ controllers.