Robust state feedback stabilization for some families of linear systems

Robust stabilization of some parametrized families of linear planar systems by means of linear state feedback is discussed. It is demonstrated that under the assumption of a polytope structure in the space of uncertain parameters, the problem reduces to a finite family of systems defined by the vertices of the polytope. It is found that if an unbounded set of solutions (feedback matrices) is required, the result is given as an explicit set of inequalities. For polytopes of pairs the problem is reducible to an equivalent one with finitely many pairs.<>