  H2-conic controller design seeks to minimize the closed-loop H2-norm for a
nominal linear system while satisfying the Conic Sector Theorem for nonlinear
stability. This problem has only been posed with limited design freedom, as
opposed to fixed-order design where all controller parameters except the number
of state estimates are free variables. Here, the fixed-order H2-conic design
problem is reformulated as a convergent series of convex approximations using
iterative convex overbounding. A synthesis algorithm and various
initializations are proposed. The synthesis is applied to a passivity-violated
system with uncertain parameters and compared to benchmark controller designs.
