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In this paper we address the problems of observer and observer-based controller design for a class of nonlinear time-delay singular systems. The proposed methods use particular Lyapunov functions depending on the disturbances in order to avoid a specific obstacle in the stability analysis. Consequently, two linear matrix inequality (LMI) conditions ensuring the H ∞ convergence of the estimation error and the closed loop system were presented. These LMIs were obtained by manipulating Young's inequality in order to linearize some bilinear terms.

In this paper, we present a new observer-based controller design method for a class of time-varying delay nonlinear systems. The key idea lies in the use of the Young's relation in a judicious manner which leads to a less conservative LMI synthesis condition. On the other hand, the Lipschitz nonlinearity of the system is treated by using a new reformulation of the Lipschitz property. This latter, exploited conjointly with the novel use of the Young's inequality, reduces the conservatism of the inferred LMI stabilization conditions for delay-independent and delay-dependent cases respectively. Finally, The effectiveness of the proposed design method is shown through a numerical example.