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Observer Based Event-Triggered Sliding Mode Control for Uncertain Chain of Integrators System

In this paper, we present the design of observer based event-triggered sliding mode control (ETSMC) for a chain of integrator system in the presence of matched uncertainties. In the scenario, where only output information is available, the observer is needed to observe all the states of the system. If a Luenberger observer is used the robustness property cannot be achieved, so it is appealing to use sliding mode observer (SMO). But conventional SMO does not give finite time convergence of all the observed states to their true values. Consequently, we use a higher order SMO (HOSMO) to observe all the states of the system in finite time. Also, to reduce computational effort, the behaviour of the system is analysed using this observer in the event-triggered environment. For this an ETSMC is proposed using these observed states and stability of the system is proved using Lyapunov analysis. It is also proved that the triggering instants generated using the proposed triggering rule do not lead to Zeno behaviour. Finally, the effectiveness of the proposed method is shown by simulation of a third order chain of integrator system.