Event-Triggered State Observer Design for a Class of Nonlinear Time-Delay Fractional-Order Systems

This paper studies the problem of designing event-triggered state observers for a class of nonlinear time-delay fractional-order systems. The time delay in the system is assumed to be unknown and non-differentiable but bounded within a closed interval. A novel discrete-time event-triggered fractional-order observer is first designed to provide an estimation vector for the state vector of the considered systems. It is ensured that the estimation vector robustly estimates the state vector of the nonlinear time-delay fractional-order systems. Then, a delay-dependent sufficient condition in terms of a convex optimization problem for the existence of the observer is established based on some lemmas relating to the Caputo derivative estimation of quadratic functions. Finally, three numerical examples demonstrate the validity of the proposed approach.