Observer-based event-triggered control for semilinear time-fractional diffusion systems with distributed feedback

This paper is concerned with the observer-based distributed event-triggered feedback control for semilinear time-fractional diffusion systems under the Robin boundary conditions. To this end, an extended Luenberger-type observer is presented to solve the limitations caused by the impossible availability of full-state information that is needed for feedback control in practical applications due to the difficulties of measuring. With this, we propose the distributed output feedback event-triggered controllers via backstepping technique under which the considered systems admit Mittag–Leffler stability. It is shown that the given event-triggered control strategy could significantly reduce the amount of transmitted control inputs while guaranteeing the desired system performance with the Zeno phenomenon being excluded. A numerical illustration is finally presented to illustrate our theoretical results.