LMI Synthesis of Parametric Robust H 1 Controllers 1

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 H1 cost. Although the performance metrics are di erent, we demonstrate that the same solution algorithm based on LMI synthesis leads to a very effective and e cient technique for real parametric robust H1 control design. Furthermore, it is di cult to compare robust H2 controllers to =Km designs, but in this work we provide insights into the issue of conservatism for various robust H1 control approaches, in particular, the Popov controller synthesis, the robust H1 design, and the =Km synthesis. The detailed analysis of these approaches is demonstrated on a exible structure benchmark problem.