Reliability and efficiency of extended linearization algorithms for general robust control problems

This paper proves that a certain class of nonconvex matrix inequalities is equivalent to linear matrix inequalities (LMIs) plus a nonconvex rank constraint. From the equivalence, this paper proposes two heuristic algorithms, that is extended linearization algorithms, to solve LMIs with a rank constraint using LMI-based approach. Reliability and efficiency of the algorithms are investigated statistically, and then extensive numerical experiments will indicate that the algorithms have decent performances from the viewpoint of computation in comparison with the existing method: the standard alternating projection method. It is also important that our approaches can be applied to a large number of other rank-minimization problems over LMIs, for example, the robust well-posedness problem which is an extension of general robust control problems.