H∞ design with pole placement constraints: an LMI approach

This paper addresses the design of H_∞ controllers that satisfy an additional constraint on the closed-loop pole location. In the state-feedback case, sufficient conditions for feasibility are derived for a general class of stability regions. These conditions are expressed as a system of linear matrix inequalities (LMI). Mixed H₂ /H_∞ design with root clustering constraints is also discussed. In the output-feedback case, similar results are obtained when the stability region is either a disk or the shined left-half plane. The validity and tractability of this approach are illustrated by a few examples