New extended LMI characterization for state feedback control of continuous-time uncertain linear systems

This paper provides synthesis conditions of robust state feedback control law for continuous-time linear time-invariant systems with polytopic uncertainty. By conveniently expressing the Lyapunov stability condition of the closed-loop system and using the elimination lemma, a new LMI synthesis condition with scalar searches is proposed. As main novelty, the scalar search is constrained to the interval (-1,1). Additionally, it is shown that the proposed relaxation contains the less conservative condition available in the literature as a particular case. Numerical examples illustrate the proposed approach.