A nonlinear robust controller design procedure is presented, which is designed to simultaneously satisfy multiple conflicting closed-loop performance specifications. Significantly, a robust performance specification for the experimental system, developed for studying the attitude control of a small-scale helicopter in our previous work, is discussed quantitatively. The robust performance specifications and nominal multiple closed-loop performance specifications are conflicting. Use of the Convex Integrated Design (CID) method can provide, where feasible, a single closed-loop controller which satisfies a set of multiple conflicting performance specifications. However, the resultant controller has a complex form. Here, the standard CID method is extended to a more general control system framework to solve the conflicting simultaneous performance design problem. When compared with the standard CID design, the extended CID design procedure generates a relatively simple closed-loop controller. Finally, the synthesised controller is tested in simulation and is validated with an experimental small-scale test helicopter, demonstrating the performance of the proposed controller.