Time delay control with sliding mode observer for a class of non-linear systems: performance and stability

Time delay control (TDC) is a type of disturbance observer (DO)-based control, where the disturbance estimation is performed by using the past information of control input and measurement signals. Despite its capability, there are concerns about its practical implementation. First, it requires acceleration measurements which are generally not available in many industrial systems. Second, input delays are introduced into the closed-loop system, but the relation between the size of the delay and the performance of TDC has not been studied. Finally, there is a lack of tools to analyze its performance in disturbance estimation and robust stability for a given set of control parameters. We construct Lyapunov–Krasovskii functionals for a class of nonlinear systems which leads to delay-dependent conditions in linear matrix inequalities (LMIs) for the ultimate boundedness of the closed-loop system. This provides a means for analyzing the trade-off between the accuracy of disturbance estimation and robust stability. To circumvent acceleration measurements, we construct a sliding mode (SM) observer where the resulting error dynamics turns into a neutral type delay system. The existence conditions of both the SM control and SM observer are provided via a single LMI. A simulation example considering the tracking control of an autonomous underwater vehicle at constant and varying speed with a comparison to a non-TDC shows the effectiveness of the proposed method.