Dynamic event-triggered prescribed-time observer via parametric Lyapunov equations

This paper is concerned with a prescribed-time observer (PTO) for a class of linear systems by using a novel dynamic event-triggered mechanism (DETM) with bounded triggering conditions. Traditional PTOs often require real-time updates of the measurement output signal, leading to high communication costs. Event-triggered approaches can address this issue. However, event-triggered approaches hardly achieve prescribed-time convergence. In order to achieve fast state estimation while maintaining low communication costs, a dynamic event-triggered prescribed-time observer (DETPTO) is developed by using a parametric Lyapunov equation (PLE), in which the estimation of all system states can also be achieved within a prescribed-time T. To achieve this goal, a DETM is proposed by integrating both estimation error and measurement error, ensuring that the observer updates the measurement output only when necessary rather than continuously. Moreover, it is proven that the proposed DETPTO can avoid the Zeno behavior. Finally, numerical simulations validate the effectiveness of the proposed methods.