Semidefinite programming tailored to H∞ optimization arising from plant uncertainty problems

An approach to H^∞ optimization using modern primal-dual and semidefinite programming techniques was introduced by Helton, Merino, and Walker (1995). In this paper the authors report results of numerical experiments with some of the algorithms introduced in the above paper. These experiments indicate that in many cases it is possible to obtain a second order convergence rate to local solutions. Also, experiments suggest that convergence rate is related to properties of optimal dual functions. On a more theoretical note, one consequence of the general theory, which we present here, is optimality conditions for μ-synthesis and D-K iteration