Parameter uncertainty is the most frequently encountered model uncertainty. Although the research on the robust control of parametric systems has a long history, existing design tools are still either conservative or not numerically efficient, particularly for the performance problems. This paper treats polytopic systems which have good compatibility with physical systems. It is shown that less conservative robustness conditions can be derived from the well-known Lagrange method by treating the performance specification as an objective function in a dilated signal space and regarding the dynamics as a hyperplane in this space. A broad class of frequency domain specifications and regional pole-placement are analyzed in detail. Desirable multiplier structures are also revealed through numerical analysis. The results lay a solid foundation for an effective robust performance design of the polytopic systems.

Owing to the bilinear nature of robust performance conditions, it remains a challenge to effectively design a controller for parametric systems. To overcome this difficulty, we establish a metaheuristic-based design framework in this paper. This framework includes a simple initialization method, detailed search flows, and the associated objective functions for each step. In addition, this method can individually and easily shape the gain characteristics of closed-loop transfer functions, thus lowering the hurdle of control design for complex and uncertain systems. The whole design procedure is validated and illustrated through its application to a drivetrain bench. Numerous trials show that on average a success rate of 70% is achieved in the search for the controller.