Reduced-order observer-based controller design for quasi-one-sided Lipschitz nonlinear systems with time-delay

In this article, the problem of reduced-order observer-based controller design for a class of nonlinear time-delay systems is addressed. First, we present sufficient conditions for the existence of the reduced-order observer of nonlinear time-delay systems. Then, a state feedback controller is designed to stabilize the systems. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the reduced-order observer-based controller. When the nonlinear part of systems satisfies the quasi-one-sided Lipschitz condition, the reduced-order observer and feedback controller can be designed separately even though the parameter (A, C) of systems is not detectable and parameter (A, B) is not stabilizable. Finally, a numerical example is presented to show the effectiveness of the proposed approach.