Convex optimization approach to observer-based stabilization of linear systems with parameter uncertainties

In this paper we investigate the design of observer-based controller for uncertain linear systems. On the basis of the approach using the Lyapunov theory jointly with linear matrix inequalities (LMIs), and by handling judiciously the Young relation, we derive new sufficient linear matrix inequality (LMI) conditions for the asymptotic stabilizability. The proposed method allows to compute simultaneously the observer and controller gains by solving only one LMI. The developed approach is then extended to both continuous-time systems with parameter uncertainties and their Euler approximation models. We show that our approach contains, as a particular solution, the elegant results established in [1]. A numerical example is provided to compare with respect to some existing methods.