PROBABILITY-ONE HOMOTOPY ALGORITHMS FOR ROBUST CONTROLLER SYNTHESIS WITH FIXED-STRUCTURE MULTIPLIERS

Continuation algorithms that avoid multiplier-controller iteration hav e been developed earlier for fixed-architecture, mixed structured sing ular value controller synthesis. These algorithms have only been formu lated for the special case of Popov multipliers and rely on an ad hoc initialization scheme. In addition, the algorithms have not used the p rediction capabilities obtained by computing the Jacobian matrix of th e continuation (or homotopy) map, and have assumed that the homotopy z ero curve is monotonic. This paper develops probability-one homotopy a lgorithms based on the use of general fixed-structure multipliers. The se algorithms can be initialized using an arbitrary (admissible) multi plier and a stabilizing compensator. In addition, as with all probabil ity-one algorithms, the homotopy zero curve is not assumed to be monot onic and prediction is accomplished by using the homotopy Jacobian mat rix. This approach also appears to have some advantages over the bilin ear matrix inequality (BMI) approaches resulting from extensions of th e LMI framework for robustness analysis.