LMI synthesis of parametric robust /spl Hscr//sub /spl infin// controllers

Abstract

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 /spl Lscr//sub 2/ gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust /spl Hscr//sub 2/ performance synthesis problem, is shown to be applicable to the robust controller design with the /spl Hscr//sub /spl infin// 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 /spl Hscr//sub /spl infin// control design. Furthermore, it is difficult to compare robust /spl Hscr//sub 2/ controllers to /spl mu//K/sub m/ designs, but in this work we provide insights into the issue of conservatism for various robust /spl Hscr//sub /spl infin// control approaches, in particular, the Popov controller synthesis, the robust /spl Hscr//sub /spl infin// design, and the /spl mu//K/sub m/ synthesis. The detailed analysis of these approaches is demonstrated on a flexible structure benchmark problem.