Event-triggered joint adaptive high-gain observer design for delayed output-sampled nonlinear systems with unknown parameters and output injection

This study presents a novel event-triggered joint adaptive high-gain observer design for delayed output-sampled nonlinear systems with output injection. These systems are characterized by the presence of unknown parameters that influence both the state and output equations. The major difficulty in designing the observer lies in the interplay between event-triggered mechanism, output injection, and time-varying delays. Additionally, the non-affine nature of the parameter’s entry into the system states equation further complicates the design. To address these challenges, a new adaptive law for unknown parameter estimation is developed under delay measurement. A novel non-Zeno dynamic event-triggered mechanism coupled with a closed-loop output predictor is proposed. The resulting observer exhibits two main features: the first one provides an input-to-state stable property, and the second one is the establishment of a theoretical condition for the inter-event time of the proposed dynamic event-triggered mechanism. The effectiveness of the designed observer is demonstrated through numerical simulations and performance comparisons with previous works.