An LMI Solution for Disk Pole Location with H-2 Guaranteed Cost

In this paper, the problem of robust pole assignment in a disk with an H-2 guaranteed cost design is addressed. The uncertain systems considered are of norm bounded type and continuous as well as discrete time. The set of gains which assigns the closed-loop poles in a disk is characterised through a Linear Matrix Inequality (LMI). A way for selecting a gain in this set, which minimises an upper H-2 norm bound on the transfer matrix between a perturbation and a controlled output, is presented. It consists in solving a convex optimisation problem with a linear criterion and an LMI as a constraint.