A new observer-based controller design method for a class of time-varying delay systems with Lipschitz nonlinearities

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.