In this paper, a new approach for fixed‐structure H2 controller design in terms of solutions to a set of linear matrix inequalities are given. Both discrete‐time and continuous‐time SISO time‐invariant systems are considered. Then the results are extended to systems with polytopic uncertainty. The presented methods are based on an inner convex approximation of the non‐convex set of fixed‐structure H2 controllers. The designed procedures are initialized either with a stable polynomial or with a stabilizing controller. An iterative procedure for robust controller design is given that converges to a suboptimal solution. The monotonic decreasing of the upper bound on the H2 norm is established theoretically for both nominal and robust controller design.
