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

Xiaoran Han*, Ibrahim Kucukdemiral, Mustafa Suphi Erden

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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. Firstly, it requires acceleration measurements which are generally not available in many industrial systems. Secondly, 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 analyse its performance in disturbance estimation and robust stability for a given set of control parameters. We construct Lyapunov-Krasovskii Functionals for a class of non-linear 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 analysing the trade-o 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 track- ing control of an autonomous underwater vehicle at constant and varying speed with a comparison to a non-TDC shows the eeffectiveness of the proposed method.
Original languageEnglish
Number of pages22
JournalInternational Journal of Robust and Nonlinear Control
Early online date14 Sep 2021
Publication statusE-pub ahead of print - 14 Sep 2021


  • time delay control
  • non-linearity-disturbance estimation
  • sliding mode controller and observer
  • linear matrix inequalities (LMIs)


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