Separation principle for quasi-one-sided Lipschitz nonlinear systems with time delay

In this article, we address the problem of output stabilization for a class of nonlinear time-delay systems. First, an observer is designed for estimating the state of nonlinear time-delay systems by means of quasi-one-sided Lipschitz condition, which is less conservative than the one-sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi-one-sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer-based controller. Under the quasi-one-sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time-delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.