Parameterized LMIs for robust H2 and H∞ state feedback control of continuous‐time polytopic systems

Summary This paper presents new extended linear matrix inequality (LMI) characterizations for the synthesis of robust H∞ and H2 state feedback controllers for continuous-time linear time-invariant systems with polytopic uncertainty. Based on a suitable change of variables and the Elimination Lemma, the proposed robust control design techniques are stated as extended LMI conditions parameterized in terms of 2 scalar parameters. One parameter is shown to belong to a bounded domain, thus limiting the scalar search domain. For the other parameter, a bounded subset is provided from numerical experiments. The benefits of the methodology are illustrated through numerical simulations performed on an uncertain model borrowed from the literature. It is shown that the proposed LMI relaxations can provide less conservative results with fewer scalar searches than some existing methods in the literature.