Event-triggered observer design for linear systems subject to delayed and sampled output

International audience; In this paper, we investigate the observation and stabilisation problems for a class of linear time-invariant systems, subject to unknown states, and network constraints, including time-delays and event-triggered sampling. A new type of event-triggered mechanism is proposed based on an appropriate storage function, which is chosen larger than the derivative of Lyapunov function. Thus, the convergence of the observer system is guaranteed by the negativity of this storage function. With the utilisation of LMI techniques and the designed novel event-triggered mechanism, as well as the utilisation of a Wirtinger-based inequality, only a slight over-estimation exists in the process of obtaining stability conditions, leading to reduced conservatism. With simulations of a mobile cart system, the effectiveness of this novel event-triggered mechanism is proven through a comparison with a classical event-triggered and also periodic time-triggered mechanisms.