Robust observer design for a class of one-sided Lipschitz systems subject to time delays and disturbances in both plants and outputs

In this paper, we consider the problem of designing state observers for a class of one-sided Lipschitz time-delay systems subject to disturbances. Not only the plants but also the outputs of the systems are subject to time delays and disturbances. The one-sided Lipschitz and quadratically inner-bounded conditions, which are more general than the traditional Lipschitz condition, are utilized to cover a broader class of nonlinearities. Based on the Lyapunov-Krasovskii approach, a robust observer design is proposed where synthesis condition is derived in terms of linear matrix inequality (LMI). A numerical example is given to show the effectiveness of the obtained results.