Linear matrix inequality–based observer design methods for a class of nonlinear systems with delayed output measurements

This article deals with observer design for a class of nonlinear systems subject to delayed output measurements. Using an observer structure borrowed from Targui et al., we propose novel linear matrix inequality conditions ensuring the asymptotic convergence of the estimation error towards zero. We demonstrate analytically that the established linear matrix inequalities are less conservative than that of Targui et al., from a feasibility viewpoint, in the sense that they tolerate larger values of the upper bounds of the delay while guaranteeing the asymptotic convergence of the observer. Such linear matrix inequality conditions are obtained due to the use of a specific Lyapunov–Krasovskii functional, the Young inequality in a judicious way and a reformulation of the Lipschitz condition in a convenient way. We provide two illustrative examples to support the efficiency and superiority of the proposed linear matrix inequality–based techniques.