A linear matrix inequality approach to the general mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// control problem

This paper presents a solution method to the general mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin//, problem, minimizing the /spl Hscr//sub 2/ norm of a closed-loop system subject to an /spl Hscr//sub /spl infin// norm constraint on another closed-loop system. It is shown that the true infimum over all internally stabilizing controllers can be approximated arbitrary closely by solving a sequence of globally convergent finite dimensional convex optimization problems over linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of this approach.