H∞ design with pole placement constraints: an LMI approach

This paper addresses the design of state- or output-feedback H_∞ controllers that satisfy additional constraints on the closed-loop pole location. Sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane. These conditions are expressed in terms of linear matrix inequalities (LMIs), and the authors´ formulation is therefore numerically tractable via LMI optimization. In the state-feedback case, mixed H₂/H _∞ synthesis with regional pole placement is also discussed. Finally, the validity and applicability of this approach are illustrated by a benchmark example