LMI synthesis of parametric robust ℋ∞ controllers

This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L₂ gain analysis of the Lur´e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust ℋ₂ performance synthesis problem, is shown to be applicable to the robust controller design with the ℋ_∞ cost. Although the performance metrics are different, we demonstrate that the same solution algorithm based on LMI synthesis leads to a very effective and efficient technique for real parametric robust ℋ_∞ control design. Furthermore, it is difficult to compare robust ℋ₂ controllers to μ/K_m designs, but in this work we provide insights into the issue of conservatism for various robust ℋ_∞ control approaches, in particular, the Popov controller synthesis, the robust ℋ_∞ design, and the μ/K_m synthesis. The detailed analysis of these approaches is demonstrated on a flexible structure benchmark problem