Extended static output feedback for robust control of linear systems with polytopic type uncertainty

This paper presents a novel approach for the controller synthesis in linear time invariant systems (LTI) with polytopical type uncertainty, by means of the extended static feedback of the measured output. The method consists of designing feedback gains for the injection of the output and its derivative, which corresponds to the control signal. Conditions for the existence of such controllers are established. The uncertainty parameters are supposed to belong to a polytope. The stabilization problem is formulated in the context of linear matrix inequalities (LMI). Multiobjective performance indices in H₂/H_∞ are also considered, which are described as LMIs. The extended H₂/H_∞ conditions are obtained by means of the well known projection lemma. Performance of the proposed synthesis technique is illustrated by numerical example.