Robust pole location by parameter dependent state feedback control

Sufficient conditions are given for the existence of a parameter dependent state feedback control assuring to a linear uncertain closed-loop system the pole location inside a circle in the complex plane. The uncertainties are supposed to belong to a polytope domain described by its vertices. The robust stabilizability condition is formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope. Extensions to cope with decentralized and output feedback parameter dependent control gains are also presented. Examples illustrate the results.