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

SUMMARY Continuation algorithms that avoid multiplier{controller iteration have been developed earlier for xedarchitecture, mixed structured singular value controller synthesis. These algorithms have only been formulated for the special case of Popov multipliers and rely on an ad hoc initialization scheme. In addition, the algorithms have not used the prediction capabilities obtained by computing the Jacobian matrix of the continuation (or homotopy) map, and have assumed that the homotopy zero curve is monotonic. This paper develops probability-one homotopy algorithms based on the use of general xed-structure multipliers. These algorithms can be initialized using an arbitrary (admissible) multiplier and a stabilizing compensator. In addition, as with all probability-one algorithms, the homotopy zero curve is not assumed to be monotonic and prediction is accomplished by using the homotopy Jacobian matrix. This approach also appears to have some advantages over the bilinear matrix inequality (BMI) approaches resulting from extensions of the LMI framework for robustness analysis.

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