An Improved Path-Following Method for Mixed ${H} _{2} /{H}_{\infty }$ Controller Design

Among the few methods available to solve bilinear matrix inequalities (BMIs) occurring in control design, the path-following method, published some years ago, appears to be one of the best ones, as far as linearization methods are concerned. However, few details are given in the literature about its implementation and limits. In this technical note, this method is applied to the design of mixed H ₂/H _infin controllers with full details of the algorithm and some improvements over the one which has been published a few years ago. The results obtained with the numerical example given in that same publication, as well as with some other examples, are compared with those given by other methods, including a direct BMI-solving program.