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 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.