ILMI algorithm for robust stabilization under structured uncertainties

An iterative algorithm with linear matrix inequalities (ILMI) is presented, for robust stabilization of linear time-invariant systems, where the uncertainty is a structured rational matrix belonging to a positive-real-like set, determined by scalar delta. The algorithm searches for a maximal set, in respect to inclusion of sets, that is, for the minimal parameter delta. A property of the algorithm is that a suboptimal solution is found in each iteration of the algorithm, and delta decreases in each iteration. Robustness in respect to the change of controller coefficients is elaborated on, and it is shown by examples that it can be greater than the robustness of the H infinity-controller. The efficiency of the algorithm, as well as its conservativity/non-conservativity, is tested on examples with random numbers.