Triple-objective dynamic output-feedback controller design via path-following

The multiobjective output-feedback controller design formulation in terms of matrix inequalities involves bilinear matrix inequalities (BMI´s). Published linearization methods, which transform these BMI´s into linear matrix inequalities (LMI´s), use the same Lyapunov matrix in all constraints, thus contain some degree of conservatism. Other approaches, such as the path-following method, have been proposed to allow the use of different matrices in the various constraints, in order to reduce that conservatism, however only for two constraints, as in the mixed H₂/H_∞ or the H₂/D-stability controller design. In this paper this approach is extended to output-feedback controller design involving three constraints, with the aim at yielding here also less conservative solutions than with existing methods. Two numerical examples show the efficiency of the proposed method.