Fixed-Structure H2 Controller Design for Polytopic Systems Via LMIs

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 discreteand continuous-time single-input single-output (SISO) timeinvariant 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 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. Copyright c ⃝ 2013 John Wiley & Sons, Ltd.