Abstract
H∞ controllers and their extensions, i.e., scaled H∞ controllers and controllers designed by µ-synthesis, are widely used for practical systems. H∞ controller design is formulated in terms of Linear Matrix Inequalities (LMIs) and the globally optimal controllers are easily designed; however, the design of scaled H∞ controllers and µ-synthesis are, in general, formulated in terms of Bilinear Matrix Inequalities (BMIs) and they require iterative algorithm (so-called D-K iteration) to obtain suitable controllers which are usually merely locally optimal controllers. The iterative procedure often stops due to its numerical instability and, in such a case, it is often the case that obtained controllers are not satisfactory with respect to design requirements. On this issue, we propose a design method in which observer-based output feedback controllers and constant scaling matrices are simultaneously optimized. Although the proposed method introduces some conservatism which comes from the structural constraints for the matrices introduced in so-called “dilation” procedure, numerical examples well demonstrate conservatism reduction thanks to the simultaneous optimization of controller gains and scaling matrices.
